# Writing equations in different forms

• Jul 9th 2010, 11:18 AM
Obiiscool
Writing equations in different forms
I have a few questions I need help with:

1. Can 2 different quadratic formulas have the same roots? Explain why or why not.

2. Write the vertex form of (x-6)(x+2)

3. Write x³+x²-6x in factor form

4. For these questions the answer on the right are incorrect, I need the correct answer written in the original form of the answer on the right.

x²+5x-24=(x+3)(x-8)
(x+2)(x-5)=x²-10
(x+3)²=x²+5

Thanks for the help in advance!
• Jul 9th 2010, 12:29 PM
Also sprach Zarathustra
For 1.

Try with Vieta's formula...
• Jul 9th 2010, 12:33 PM
Mathelogician
Hi.

1-No. if for ax²+bx+c= 0 the roots are x1 and x2 and for dx²+ex+f the roots are y1 and y2, we know that x1=y1 and x2=y2 (because we assumed that they have the same root) and by using the fact that: for a quadratic equation ax²+bx+c= 0 which its roots are x1 and x2, we have x1 * x2=c/a and x1 + x2=-b/a, We see that at last, the components of the equations will be equal!
3- x³+x²-6x =x(x²+x-6)= x(x-2)(x+3)
4-
x²+5x-24=(x-3)(x+8)
(x+2)(x-5)=x²-3x-10
(x+2)(x-5) is the same last one!
• Jul 9th 2010, 12:51 PM
Obiiscool
Thanks for those man. The last one was supposed to be this:

(x+3)²=x²+5
• Jul 9th 2010, 12:56 PM
Mathelogician
So: (x+3)²=x²+6x+9
• Jul 9th 2010, 01:05 PM
Obiiscool
Thanks. Anybody know how to write the vertex form of (x-6)(x+2)?
• Jul 9th 2010, 01:24 PM
Mathelogician
The vertex form of an equation is given by the formula: f(x) = a(x-h)^2 + k Where (h,k) is the vertex.
So for yours: (x-6)(x+2) = x^2-4x+12 = (x-2)^2+8. Then the vertex form is: (2,8).