If f(x)=x^2+bx+c has roots -5 and 7 then the exact value of b is ___. and the exact value of c is ___.?

Question

If f(x)=x^2+bx+c has roots -5 and 7 then the exact value of b is ___. and the exact value of c is ___.

Answer 1

From the root -5, we have

0 = (-5)² + b(-5) + c

0 = 25 - 5b + c

5b - c = 25 [Equation 1]

From the root 7, we have

0 = (7)² + b(7) + c

0 = 49 + 7b + c

7b + c = -49 [Equation 2]

You can use either Elimination or Substitution Methods to solve for b and c.

I'll use Elimination.

Equation 1 + Equation 2 :

12b = -24

b = -24/12 = -2

Sub back into Equation2:

7(-2) + c = 49

c = 49 + 14 = 63