for which equation does the sum of the roots equal 8 and the product of the roots equal -2?1) x^2-8x-2=02) x^2-8x+2=03) x^2+8x+2=04) x^2+8x-2=0please show me how
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