Solving a Quadratic Equation: Finding All Linear Factors

In summary, the conversation discusses using synthetic division to find linear factors of a polynomial and clarifies the correct arithmetic needed to solve the problem. The conversation also mentions using the quadratic formula for quadratic equations.
  • #1
DumbKid88
4
0
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?

Please Help!
 
Last edited:
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  • #2
Too tempted to make a dumb joke, but I'll wait. :biggrin:

PS: Dk88, welcome to PF! Are you having trouble posting? Have you read the forum guidelines?
 
  • #3
Sorry i accidentally posted it when I was just trying to preview it.
 
  • #4
Check your arithmetic [tex]-17 + 2 \ne -19[/tex]

Then when you get a quadratic apply the quadratic formula.
 
  • #5
SnipedYou said:
Check your arithmetic [tex]-17 + 2 \ne -19[/tex]

Then when you get a quadratic apply the quadratic formula.

And that, my friend, is why my name is DumbKid. Ya -3 +4 surely is not -1. Thanx for the help.
 

FAQ: Solving a Quadratic Equation: Finding All Linear Factors

What is a quadratic equation?

A quadratic equation is an equation in the form of ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. It is a polynomial equation of degree two and can have one or two real solutions.

How do you solve a quadratic equation?

To solve a quadratic equation, you can use the quadratic formula, factoring, or completing the square. The quadratic formula is the most commonly used method and is given by x = (-b ± √(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients of the equation.

Why is it important to find all linear factors of a quadratic equation?

Finding all linear factors of a quadratic equation allows us to fully understand the behavior of the equation and determine its roots or solutions. It also helps in graphing the equation and identifying its maximum and minimum points.

Can a quadratic equation have only one solution?

Yes, a quadratic equation can have one, two, or no real solutions. A quadratic equation with only one solution is called a perfect square trinomial and can be written in the form of (x + k)^2 = 0, where k is a constant.

Are there any real-life applications of solving quadratic equations?

Yes, quadratic equations are widely used in physics, engineering, and economics to model real-life situations such as projectile motion, freefall, and profit optimization. They are also used in the fields of computer graphics and game development to create realistic curves and shapes.

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