Quadratic equation Definition and 252 Threads

1. Problem Barkley runs a canoe-rental business on a small river in Pennsylvania. Currently, the business charges $12 per canoe and they average 36 rentals a day. A study shows that for every $.50 increase in rental price, the business can expect to lose two rentals per day. Find the price...

1.given the equation a(3x2+2x+1)=4x-6x2-4 with the solutions x1 and x2 a) let a=0 without solving the equation calculate x1-3+x2-3 the correct answer is supposed to be -7/2 Homework Equations x1+x2=-b/a x1*x2=c/a The Attempt at a Solution The first thing I was that I put in...

Problem: If the curve $y=ax^2+2bx+c$, ($a,b,c \,\in\,\mathbb{R},\,a,b,c \neq 0$) never meet the x-axis, then a,b,c can't be in A)Arithmetic Progression B)Geometric Progression C)Harmonic Progression D)All of these Attempt: Since, the curve never meets the x-axis, we have the condition...

consider the equation: ax^2+bx=c imagine that the constant c is divided into to parts: c=Z+Y where ax^2= Z and bx=Y so basically could we say c is part area and part length?? Sorry if the question is not explained better but that's the best way I came up with to describe it.

I know for ##ax^2+bx+c=0##, x=\frac{-b^+_-\sqrt{b^2-4ac}}{2a} Using ##x^2-3x-4=0##, we know it is equal to ##(x+1)(x-4)=0##. So ##x=-1## or ##x=4##. but using the formula: x=\frac{-b^+_-\sqrt{b^2-4ac}}{2a}=\frac{3^+_-\sqrt{9+4}}{2}=\frac{3^+_-\sqrt{13}}{2} I cannot get -1 and 4...

Hi, I am trying understand if there is a quick way to figure out the impact of the X term in a quadratic equation. For example, by looking at the following equation, I know that it is a parabola (X^2) ; by looking at 24, I know that it is the y-intercept. However, I don't know what is the...

Homework Statement If the quadratic equation ax2+bx+c=0 has equal roots where a, b and c denote the lengths of the sides opposite to vertices A, B and C of a triangle ABC respectively, then find the sum of integers in the range of $$\left(\frac{\sin A}{\sin C}+\frac{\sin C}{\sin...

Solve the following quadratic equation. Use factorisation if possible. X2 - 4X - 8 = 0 Normally I wouldn't have trouble factorising a quadratic, but I have just been introduced to a new way to do it and I want to use this way to answer the question. Here's how far I get, then I'm unsure what...

Homework Statement In the expression x2 + kx + 12, k is an integer and k < 0. Which of the following is a possible value of k? (A) –13 (B) –12 (C)  –6 (D)   7 Homework Equations I know it uses the a.c method of factorization but don't know how to use it? The Attempt at a...

1) Find the range of values of k such that the function f(x) \equiv k(x+2)^2-(x-1)(x-2) never exceeds 12.5. I've missed several stages of the computation because it is quite lengthy. I hope you get the flow of things. My attempt... (k-1)\left[ x + \left( \frac{4k+3}{k-1} \right)x +...

Help! Using 3 Points to Find Quadratic Equation in General Form I have a quadratic equation question that I have to solve, but I can't seem to understand it. The question is: "Using points (1,0);(3,0);(0,-6), find the quadratic formula in General Form (ax^2 + bx + c). My teacher says...

Homework Statement A ball is thrown at 72km/h speed from top of a building. Building is 125m tall. Homework Equations Distance traveled before it hit the ground is as follows: s = Ut + 0.5 gt^2 The Attempt at a Solution Using quadratic equation: x = -b±b^2 - 4ac / 2a The...

Homework Statement The total number of integers that satisfy the equation x2-4xy+5y2+2y-4=0

The no. of Real Roots of the equation $\displaystyle \frac{\pi^e}{x-e}+\frac{e^\pi}{x-\pi}+\frac{\pi^{\pi}+e^{e}}{x-\pi-e} = 0$ My try:: Let $\displaystyle f(x) = \frac{\pi^e}{x-e}+\frac{e^\pi}{x-\pi}+\frac{\pi^{\pi}+e^{e}}{x-\pi-e}$ Now we will take a interval $x\in \left(e\;,\pi\right)$...

Solve (m-2)x^2-(m+3)x-2m-1=0.

So here is the question: 2x/7=2x^2

Here is the question: Here is a link to the question: Solve the quadratic equation? - Yahoo! Answers I have posted a link there so the OP can find my response.

Homework Statement Homework Equations x(2x^2 - 5) = -1 The Attempt at a Solution This question has been flung at me without any pre-examples how to solve it. I have only dealt with equations like 2x^2 + 5x - 12 = 0. I know that the equation above should be set to zero, but how...

A force F=(cx-3.00x2)i acts on a particle as the particle moves along an x axis, with F in Newtons, x in meters, and c a constant. At x = 0 m, the particle's kinetic energy is 18 J; at x = 5 m, it is 12 J. Find c. F=ma KE=1/2mv2 I guess I don't understand the relationship between force...

Homework Statement Actually, it is told by one of my friend. He asked for the answer of this quadratic equation. m^3-m^2+2=0 Homework Equations m^3-m^2+2=0 The Attempt at a Solution But, I think we need one more equation to solve it. Is there any way to solve it by only...

Homework Statement Solve for x_1^6+x_2^6 for the following quadratic equation where x_1 and x_2 are the two real roots and x_1 > x_2, without solving the equation. 25x^2-5\sqrt{76}x+15=0 Homework Equations The Attempt at a Solution I tried factoring it and I got...

Homework Statement If the roots of x^2 - 2x + 4 = 0 are x1 and x2, what is x1^2 + x2^2? Homework Equations The Attempt at a Solution I don't think these questions can be answered by solving for x only cause there will be no real root(complex number). So I found that x1 + x2 =...

Homework Statement Solve 4y-y2=x for y. The Attempt at a Solution First I tried using the quadratic equation with a=-1 b=4 c=-x y=(-b±(42-4(-1)(-x))(1/2))/2(-1) That got me this far: y=2±(8-2x)(1/2) Then I checked wolfram and now I am confused . Did I not approach this corectly?

Homework Statement 3x2-8x-1=0 Homework Equations The Attempt at a Solution So here i attempt to solve the equation...usually the way i go about this is you multiply 3 by -1 you get -3 then i ask myself what multiplies to -3 and adds to -8...after that i am able to solve...

Prove that 12x-8-3x^2 can never be greater than 4. How do you prove? Do you find he discriminant? But isn't discriminant for roots only not equations?

Homework Statement So I've worked this problem for awhile. Its a several page of math problem with optimization, legrangians, cramers rule, etc to get to this point. All I need to do now is by hand solve this equation for x and y with the constraint. Homework Equations -0.03x^2 + 40x...

Solve for $x$: $$4x^2 +4xy - 6y - 9 = 9 $$

Homework Statement Folks, I wish to construct a quadratic expression from a graph which has the following 2 coordinates. ##(0,0)## and the vertex ##(\alpha h_e,1)## where ##0<\alpha<1## Homework Equations Using the following ##y(x)=a(x-h)^2+k## The Attempt at a Solution...

Hi everyone, Can someone please tell me how to find the factors of the below quadratic equation? 3x^2 - 9x + 4 = 0 I had already tried to find them by using the below method and wasn't able to continue further because of I do not understand. Huygen (3x^2 - 7x + 4) -2x = 0 (3x-4)(x-1)-2x=0

Homework Statement Use algebra to find the x-intercepts and y-intercept of The graph of y=-x^2/5+x/5+6 this is a parabola. Homework Equations y=-x^2/5+x/5+6The Attempt at a Solution Find the y-intercept , which is substitute 0=x into the equation to find the answer , done that . The problem...

How do we graph a quadratic equation in the form ax^2+bx+c =0?, or an equation like , f(x)(or y)= [(x+b/2a)^2 - (D/4a^2)], where D = b^2 - 4ac? or how do we get a parabolic curve intersecting at its roots(of the quadratic equation) in the x axis?

(x+3)(x-4)(x-2)(x+1) = 24 Can we change it into a quadratic equation without multiplying the expressions under those brackets?

Homework Statement If α and \frac{1}{αα}are the roots of the equation 5x^{2}+13x+k then k will be: a) 5 b) -5 c) 13 d) 1 Homework Equations The Attempt at a Solution I've tried multiplying both the roots to get \frac{c}{a} and adding the roots to get...

I am trying to figure out how the coeffecients in the general second degree equation transform the function as they change through a range of values. I think that d and e are the proportion of x and y are horizontal and vertical shifts, but less sure about a, b, and c. Here is the equation as...

Homework Statement 1. Neglecting the height of release, a ball is thrown vertically upwards at 20 m/s, find: d) time (s) that the projectile is at height 10.5 m. V1 = 20m/s a = -9.81m/s^2 d = 10.5m Homework Equations d = v1*t + 1/2 a(t^2) The Attempt at a Solution...

Homework Statement Find all the values of 'a', so that exactly one root of the equation x2-2ax+a2-1=0, lies between the numbers 2 and 4, and no root is either equal to 2 or equal to 4.Homework Equations The Attempt at a Solution Let f(x)=x2-2ax+a2-1 I tried to visualize the question by graph...

Homework Statement For a constant k, consider the function f(x) = x2 + kx + k2 - 2k - 4 Find the range of k for which f(x) = 0 has one solution between 0 and 1 and the other solution between 1 and 2Homework Equations quadratic formula discriminantThe Attempt at a Solution x2 + kx + k2 - 2k - 4...

Hey, I was going through some mechanics notes and came across this quadratic equation to solve for x. In my notes it is supposed to equal 3 however I do not get that result. I am not sure if I am simplifying it wrong or what. I am ending up with 2.12 for the positive value. Please let me...

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Homework Statement Find all solutions to z^2 + 4conjugate[z] + 4 = 0 where z is a complex number. Homework Equations Alternate form: 4conjugate[z] + z^2 = -4 The Attempt at a Solution I have tried solving this solution using the quadratic formula. However, √b^2 - 4ac = √16 - 4x1x4 = 0...

solve √(5x-1) - √x=1 eq. 1 transpose one of the radicals: √(5x-1)=√x+1 Square: 5x-1=x+2√x+1 Collect terms: 4x-2=2√x or 2x-1=√x Square: 4x^2-4x+1=x, x=1/4 , 1. x=1/4 is not the root by substitution to equation 1. ... My question what makes x =1/4 is not the root, only x=1 is the root.

if $f(x)$ be a continuous and assumes only rational values so that $ f(2010) =1. $ then roots of the equation $f(1)x^2 + 2f(2)x + 3f(3) =0$ are

I have to find the vertex, axis, domain, & range of this quadratic equation: f(x)= -1/2(x+1)^2 -3 I can't remember how to do the vertex. Is it y= -b/2a? Also, I tried factoring the equation, but I think I messed up. I ended up with: f(x)= .25x^2 +.5x-2.75 Thanks

Homework Statement Let the roots of x2 + x + 1 = 0 be \alpha and \beta, form a quadratic equation with roots: (i) \alpha2, \beta2; and (ii) \frac{1}{\alpha}, \frac{1}{\beta}.The attempt at a solution sum of roots = \alpha + \beta = -1 product of roots = \alpha\beta = 1 (i) sum of roots =...

Homework Statement For each of the following, identify the base function and describe the transformation(s): f(x)=-4(3x)^2 + 5 Homework Equations f(x) = -4(3x)^2 + 5 The Attempt at a Solution Alright so my attempt at figuring out the requested answers are: Base function = x^2...

Homework Statement I'm studying for the GMAT and the study materials do not include how to solve this equation. I need to know how to solve it without a calculator. Homework Equations If 2^x - 2^x-2 = 3(2^13), what is the value of X? The Attempt at a Solution The answer key says...

Homework Statement Rotation of axes to Eliminate the xy-term in a quadratic equation 3x^2 - 10xy + 3y^2 + 16 √2x - 32 = 0 2. The attempt at a solution I do not know the method that should be taken to solve this sort of question. That is what I am looking for. If anyone can point me...

Homework Statement Homework Equations distance = rate * time The Attempt at a Solution So the speed of the ball I have as: [t = time] 5 + 32t Which I believe makes sense because the ball is initially traveling @ 5 ft/sec, and after 1 second, the ball is traveling 37...

Homework Statement Hello! z^2 - (7+2i)z + (12+8i) = 0 The Attempt at a Solution I used the quadratic equation and got: z = (7+2i)/2 +- sqrt( -3/4 - i) r = 5/4, and the argument is Theta = arctan(-1/-3/4) = 0.927 925 - Pi (since x < 0 and y < 0, right?) Then, I know that z =...

Homework Statement The following equation defines a rational function.Find its Range f(x) = x2/(x-1) The attempt at a solution Let y = x2/(x-1) =>y(x-1) = x2 =>xy-y = x2 =>x2-xy+y = 0 comparing with the general form of quadratic equation ax2+bx+c = 0, a=1, b=-y, c=y...