Question

Find all real zeros of the function. h(x)=4(x²-36)(x+7)²(x-7)

Answer 1

To find the real zeros of the function h(x) = 4(x² - 36)(x + 7)²(x - 7), set the function equal to zero and solve for x: x = -7, 6, 7.

Step-by-step explanation:

To find the real zeros of the function h(x) = 4(x² - 36)(x + 7)²(x - 7), we set the function equal to zero and solve for x:

1. Set h(x) = 0 and expand the function: 4(x² - 36)(x + 7)²(x - 7) = 0
2. Apply the zero product property and set each factor equal to zero:
   a) x² - 36 = 0
   b) x + 7 = 0
   c) (x - 7) = 0
3. Solve each equation for x:
   a) x² - 36 = 0
   Solution: x = ±6
   b) x + 7 = 0
   Solution: x = -7
   c) x - 7 = 0
   Solution: x = 7

Therefore, the real zeros of the function h(x) = 4(x² - 36)(x + 7)²(x - 7) are x = -7, 6, 7.