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for which equation does the sum of the roots equal 8 and the product of the roots equal...

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swavers | Student, Grade 11 | eNoter

Posted January 27, 2011 at 8:01 AM via web

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for which equation does the sum of the roots equal 8 and the product of the roots equal -2?

1) x^2-8x-2=0
2) x^2-8x+2=0
3) x^2+8x+2=0
4) x^2+8x-2=0

please show me how

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted January 27, 2011 at 8:17 AM (Answer #1)

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If f(x)= ax^2 + bx + c and x1 and x2 are the roots.

==> x1+x2 = -b/a

==> x1*x2 = c/a

In all 4 cases we have a= 1

==> x1*x2 = -b

==> x1*x2= c

Let us test the roots we have.

Given that x1+x2 = 8 = -b ==> b = -8

Also, given that x1*x2 = -2 ==> c = 2

Then the quadratic equation is:

f(x) = x^2 + 8x +2 = 0

Then, the answer is:

3) x^2 + 8x +2

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