Question

Wilma and Greg were trying to solve the quadratic equation: x^2 + bx + c = 0

Wilma wrote down the wrong value of b (but her value of c was correct), and found the roots to be 1 and 6. Greg wrote down the wrong value of c (but his value of b was correct) and found the roots to be -1 and -4. What are the actual roots of x^2 + bx + c = 0?

Answer 1

roots of 1 and 6 mean: (x - 1) (x - 6) = 0
this expands to: x^2 - 7x + 6 = 0

then roots of -1 and -4 mean: (x + 1) (x + 4) = 0
this expands to x^2 + 5x + 4 = 0

Answer 2

so we take Wilma's c value and Greg's b value
b = 5
c = 6

Answer 3

x^2 + 5x + 6 = 0

6 = 2 x 3
2+3 = 5

x^2 + 2x + 3x + 6 = 0 [factor by grouping]
x(x+2) + 3(x+2) = 0
(x+2)(x+3) = 0

Answer 4

so the roots are -2 and -3