Quadratic equation Definition and 252 Threads

Homework Statement Solve the equation ax2 + bx + c = 0. The following are the given information: (a) a = 1 (b) One root is twice the other root. (c) c = 2 You are NOT required to solve the problem but to decide whether: 1) The given information is all needed to solve the problem. In...

I've been having trouble understanding why my answers are always different to the solutions and I found that there's two equations: {-b ± SQRT(b^2 - 4ac)}/2a and {-b ± SQRT(b^2 -ac)}/2a I don't know when to use either equation, always having used the first, and for someone at my level to...

If a(12a+5b+2c)>0 and the equation ax^2+bx+c=0 has roots y and z , then find out the range of the roots of the equation ...

An object accelerates at the rate of 1.30 m/s^2 over a displacement of 11.8m, reaching a final velocity of 7.00 m/s. For what length of time was it accelerating? Explain the answers. NOTE: Actually, when I first was about to post this, I finally had gotten the answer I needed. However, I cannot...

Homework Statement A light bulb is wired in series with a 144Ohm resistor, and they are connected across a 120.0-V source. The power delivered to the light bulb is 23.4W. What is ther resistance of the light bulb? Note that there are two possible answers. Homework Equations P = I^2R...

[b]1. Suppose y = bx^2 +cx + a a.) in terms of a, b, and c, what values of x make y=0? b.) if a=3.1, b= -2.2 and c=-4.3 evaluate those solutions to 3 significant digits: Homework Equations [b]3. I am not really sure how to solve for what the question is asking for in part...

Homework Statement I have a probability distribution function (PDF) going fromi 0 to a on the y-axis and 0 to 30 on the x-axis. The function describing the PDF is the quadratic equation f(x) = a+bx+cx^2 I have to find a, b, and c. Homework Equations The Attempt at a Solution...

k so i used x-xo= Vo t + 1/2 at^2 plugged in all my values then moved everything to one side and used the quadratic formula here is my question. when i solve for it i get t=40.28 and t= 40.58 So which t is my time?

Quadratic equation without numbers?? How would one go about solving an equation such as B2X2+2ABCX-ABC2 for the value of x that equals zero? All of the letters are constants except for X, so would this be a quadratic equation problem.? The solution in the book is somehow...

1. Consider the quadratic equation ax^2+px+aq+q=0 where a does not equal to zero & p and q are constants . It is known that one of the roots of the quadratic equation is always 1 regardless of the value of a. Prove that p+q=0 [b]3. I have tried to factorize it and it became x(ax+p)+q(a+1)=0...

Homework Statement 2 cos x + tan x = sec x Homework Equations I can move terms around with identities, but I'm stuck with the partially solved equation below. I don't know how to solve a quadratic with weird terms. I got really far. But how do I show sin x? sin x = (-1 +- sqrt...

Hey I'm wondering if anyone can give me a proof to the quadratic equation solution which is not the simple add here multiply that proof (I just recall some cooler proof, which I think requires more "complicated" mathematics than adding and multiplying, though I can't remember what it was)

X^2(2a – bX^2) = 2 value of constants can be pre-determined as a =0.8466 & b= 0.1733. Find X?

HI Can anybody tell me how to calculate a PDF of y, where y is a function of x, such that y = a X*X + bX + C (i.e. a quadratic equation), and X follows the Normal Distribution X ~N(0, sigma) Help anybody? Thanks

here is my task: (x³-4x²+5x-2):(x-1)= We did such task in school but I didn't got it .. Here is the task that we did in school (x³-3x²-6x+8) :(x-1)= x²- 2x-8 but I don`t get it why x² is the result and why 3x² ?? Can someone help me? Thank you in advance

Question: Find the coefficient of x^5 in (1+x+x^2)^4. Problem: I have not come across expanding brackets which have x^2. I know how to apply the binomial theorem for (a+b)^n or (1+a)^n but have not come across (1 + ax + ax^2)^n. They are not explained in my textbooks so I was wondering if...

Show that the equation x2 + (3\alpha - 2)x + \alpha(\alpha - 1) = 0 has real roots for all values of α \in IR. How do i do this? Do i just use the b2 + 4ac \geq 0 ?

Homework Statement If one root of a quadratic equation with rational co-efficient is (2^(1/2)+1) , then find the quadratic equation. Homework Equations x=(-b+d^1/2)/2a d=b^2-4ac The Attempt at a Solution Well, I can't quite understand this question. Please help me to...

I know this is a simple question but for some reason I am getting stumped: Question: x-3=-x^2 atempt: (x^2)+x = 3 x^2 + x + 1/4= 3(4) + 1/4 (x+1/2)^2= 3 root everthing x+1/2= root 3 x=+,- root 3 -1/2

Hi All, I have a semantics question. Why is the quadratic equation called what it is? A polynomial of degree two is called a quadratic polymonial but I've always associated the root quad to mean four! Thanks in advance. Bob:smile:

who came up with the Quadratic equation and what is the proof behind it?

Homework Statement y^2 - 2y = x^3 + 2x^2 + 2x + 3 Homework Equations The Attempt at a Solution Solve for y How do you solve for y? my book says since that equation is quadratic in y, it can be solved as y = 1 +- sqrt(x^3 + 2x^2 + 2x + 4) but I have no idea how to do that...

Ok this should be pretty simple math for you guys (Sophomore in HS) Given that x-2 is a factor of P(x)=2x^3-3x^2-17x+30, find all other linear factors. I started out doing synthetic division, and got 2x^2-x-19 with remainder -8. Shouldn't the remainder be zero since x-2 is a factor...

Ax^2+Bx+C=0 PROGRAM delta1 IMPLICIT NONE REAL :: A,B,C REAL :: DELTA,X1,X2 PRINT *,"Enter the a,b,and c" READ *,A,B,C delta=b**2-4*a*c IF (delta>0)THEN PRINT *,"The roots are real" X1=(-B+SQRT(DELTA))/(2*A) X2=(-B-SQRT(DELTA))/(2*A) PRINT *,"X1 = ",X1,"X2 = ",X2...

Homework Statement basically I am suppose to linearize d=vit + 1/2at^2 into d/t^2 vs 1/t, t/d vs t^2/d and 1/d vs 1/t and its asking which graphs would be linear and non-linear. Homework Equations d=vit + 1/2at^2 The Attempt at a Solution all i know is that in order to linearize this i...

This is a simple word problem that I just can't wrap my head around. The answers are 7 and 9: The sum of two numbers is 16, but the sum of their squares is 130. Find the numbers. I am supposed to use a quadratic equation as a means to solve the question, and all I need to do is to create...

Hi, How to find the equation if one root of a quadratic equation is 1 + 3i. Regards, Suganya EasyCalculation ToFocus

Homework Statement How to find the conditions on the coefficients of a quadratic equation for the roots to be outside the unit circle eg bx^2 + x - 1 = 0 where b is a constant How do we find the condition(s) that b must satisfy such that the roots of the quadratic lie outside the unit circle...

Homework Statement I have the following question to answer: Show that (X^2/h^2)*((1/2*y1) - y2 + (1/2*y3)) + (X/h)*((-1/2 y1)+(1/2 y3))+y2 (sorry about the format) is equal to (taylor expansion): y = y2+(x(dy/dx)¦0 + (x^2/2*((d^2)y)/(dx^2))¦0 Homework Equations also given in...

I might not be the brightest bob in the bunch but I am having trouble with a simple quadratic equation. k^2 + (k + 4)^2 = 346 According to my manual expands to: k^2 + k^2 + 8k + 16 = 346 Everything is going fine until I see the 8k. Where did the 8k come from? Or is my...

Now I am trying to graph this thing. Lets say I have x^2+x+10=0 So yah... I plot them for -10<x<10 and get the y values... What I would like to know is how do I change the scale as to get zoom in and zoom out effect?

the book asks to fnd the four roots of z to the fourth power + 4 = 0 and then use to demonstrate that z to the fourth power + 4 can be factored into two quadratics with real coefficinets. I am clueless on where to start. Please help.

y^2 = 4(x+4)^3 0<=x<=2 ...y>0 Ok..so do I just simplify it to y=etc... and then find the derivative and solve..I tried this and I get a kinda long derivative..just seems like it should be easier? Thanks

Please Help! I designed this "PROGRAM"! TO calculate the real roots of a quadratic equation... but the compiler miracle C kept saying there's something wrong around the "if" word... saying "unrecognised types in comparison" it seem SO FINE to me... what is wrong?!:eek: #include...

Hey. Today i had a test on quadratics and discriminants. I think i did fairly well, but i am a bit confused about one of the questions i had in it. We were given the following quadratic equation: 12x^2 + 8mx + (4m-3) = 0 What we had to do was prove that for any integer value of m, the...

Hey. I've got a question to solve, and I am a bit confused. Ok. I understand what the question is asking, i just don't know how to do it. I am oretty sure that if \delta < 0, thenthere are no real solutions, but I am not sure about 1 or 2 solutions. I played around with quadratic functions...

I'm supposed to use this equation: y = x^2-8x+7 To solve the following questions: 1) What is the value of the discriminant? 2) Find the roots by factoring and solving. 3) Find the roots by using the quadratic equation. Can anyone give me some help? Thanks! :)

Ok, the question I have is attached. What I have done is found the general solution: (Question was seperable, so it was easy) y = x^2 - 2x + c But I don't kwow what/how to do is finding the initial conditions where there are: (a) No solutions (b) more than one solution (c) precisely...

Hi, I just need to learn in drawing graphs using a quadratic equation. Also I need to know how to find the minimum and maximum point and the line of cemetry from the equation (I need to know by proving it in the equation) Has anyone got any website to clearly learn about this? I know...

Hello All I am trying to figure out how to determine if there are two, one, zero, or infinitely many roots for given formula ax^2 + bx + c. Are there any easy ways to determine this without having to use the quadratic formula? Thanks P

Hi! I'm new here so if this has been covered please accept my apologies. I'm having trouble proving the equation from: ax²+bx+c=0 to the solutions x=(-b(+/-)√b²-4ac)/2a I've been told to complete the sqaure of ax²+bx+c, then rerrange to give x, but I just can't get it! If you could show the...

Students from a history class prepare a trip that will cost them a total of $189 that will be shared between them. The day before the trip, 6 students discovered that they can't participate in the trip. To avoid cancellation, the rest of the class decided to pay an additional $2 each. How many...

Hey, could someone please help me with this problem? I just want to know why the graph of Quadratic Equation are symmetric and why does the maxima and minima ( = -b/2a ) the mean of the two roots? One more thing I didn't get was what does the a represent in ax2+bx+c ( ax square+bx+c)? I know for...

Hi, I may not be thinking straight or something, and I am having trouble with this question, please help!: Given that 'p' is real, find the set of values of 'p' for which the roots of: (2p+1)x^2 - 10x + p-2 = 0 a) Are real b) Have a sum>5 Im thinking along the lines of: alpha+beta =...

I'm having some trouble figuring out how to simplify the following problem. I know that i= the sq root of -1, and that i^2=-1, but I'm not sure how to approach this problem. sq.rt.(-x^2-4x-3)

I have this multiplication problem it says solve 11sin theta-7=3-6sin^2 theta algebraically for the domain 0<=theta<=2pi I rearranged this into a quadratic formula equal to 0 6sin^2 theta+ 11 sin theta -10=0 common factored this and then got 2sin theta=0 and 3sin theta -2=0 isolating...

heres a problem i stumbled: find three rational numbers a,b,x such that: x^2 + 5 = a^2 x^2 - 5 = b^2

Hellooooo everybody. i have a very distinct feeling that there's something very wrong here... OK, what I'm trying to do is to get to the quadratic equation through the standard form of a polynomial equation in the second degree. :smile: watch this, and go to this website. it lists the...

Hi, Please Can You Help Me To Understand How To Find The Vertex Of A Quadratic Equation (x,y Coordinates) Just By Looking At The Equation ? Eg What Is The Vertex Of Y=3x^2+4x+7 ? __________________________________________________ Also, How Do I Transform A Straight Line Graph...

Dear members, For the general equation ax^2 + BX + C = 0 , what does increasing/decreasing the a, b and c values do to the graph ? Are they related to each other or not ? If C was 0 will the graph always be symmetrical about the origin or is this my misunderstanding ? Thankyou...