Question

find all the zeros of the quadratic function.
y = x² - 10x - 24
if there is more than one zero, separate them with commas.
if there are no zeros, click on
one\.
zero(s):

Explanation:

Step1: Set y=0 to find zeros

To find the zeros of the quadratic function \( y = x^2 - 10x - 24 \), we set \( y = 0 \), so we have the equation \( x^2 - 10x - 24 = 0 \).

Step2: Factor the quadratic equation

We need to factor the quadratic expression \( x^2 - 10x - 24 \). We look for two numbers that multiply to \( -24 \) and add up to \( -10 \). The numbers are \( -12 \) and \( 2 \) because \( -12 \times 2 = -24 \) and \( -12 + 2 = -10 \). So, we can factor the quadratic as \( (x - 12)(x + 2) = 0 \).

Step3: Solve for x

Using the zero - product property, if \( (x - 12)(x + 2)=0 \), then either \( x - 12 = 0 \) or \( x + 2 = 0 \).

• If \( x - 12 = 0 \), then \( x = 12 \).
• If \( x + 2 = 0 \), then \( x=-2 \).

Answer:

\( 12, - 2 \)