Question

Manny was given the equation (x+2)(x-17)=0 and asked to find the zeros. The solutions he came up with were x=2 and x=-17. Are his solutions correct? Justify your answer.

Answer 1

no

Explanation:

Neither "solution" satisfies the equation.

For x=2,

(2 +2)(2 -17) = 4(-15) = -60 ≠ 0

For x=-17

(-17+2)(-17-17) = (-15)(-34) = 510 ≠ 0

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Solutions are values of x that make the factors 0.

x + 2 = 0 . . . first factor = 0

x = -2 . . . . . . subtract 2 from both sides of the equation

x -17 = 0 . . . . second factor = 0

x = 17 . . . . . . .add 17 to both sides of the equation

Appropriate solutions are x = -2 and x = 17.