Question

The zeros of the function p(x) = x2 – 2x – 24 are

Answer 1

Answer: x = 6, x = -4

Step-by-step explanation:

Find two numbers whose product is the c-value (-24) and sum is the b-value (-2):

0 = x² - 2x - 24

                    ∧

                   1 -24

                   2 -12

                   3  -8

                   4  -6 = -2    This works!

0 = (x + 4)(x - 6)

Apply the Zero-Product Property (set each factor equal to zero and solve)

0 = x + 4      0 = x - 6

-4 = x            6 = x

Answer 2

The zeros of a function are the value of x, when the function equals 0

The zeros of $\mathbf{p(x) = x^2 - 2x - 24}$ are 6 and -4

The function is given as;

$\mathbf{p(x) = x^2 - 2x - 24}$

Expand

$\mathbf{p(x) = x^2 +4x- 6x - 24}$

Factorize

$\mathbf{p(x) = x(x +4)- 6(x + 4)}$

Factor out x + 4

$\mathbf{p(x) = (x -6)(x + 4)}$

Set to 0

$\mathbf{(x -6)(x + 4) = 0}$

Split

$\mathbf{x -6 = 0\ or\ x + 4 = 0}$

Solve for x

$\mathbf{x = 6\ or\ x = -4}$

Hence, the zeros of $\mathbf{p(x) = x^2 - 2x - 24}$ are 6 and -4

Read more about zeros of functions at:

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