Question

If f(x)=x³-7x²-14x 48 f(x)=x 3 −7x 2 −14x 48 and f(8)=0f(8)=0, then find all of the zeros of f(x)f(x)?

A) x=8,x=−2,x=3
B) x=8,x=2,x=−3
C) x=−8,x=2,x=3
D) x=−8,x=−2,x=−3

Answer 1

To find the zeros of the function f(x) = x³ - 7x² - 14x + 48, we can set the function equal to zero and solve for x using the quadratic formula.

Step-by-step explanation:

To find the zeros of the function f(x) = x³ - 7x² - 14x + 48, we can set the function equal to zero and solve for x. Rearranging the equation, we get x² + 0.0211x - 0.0211 = 0.

Using the quadratic formula, with a = 1, b = 0.0211, and c = -0.0211, we can solve for x:

x = [-b ± √(b² - 4ac)] / (2a)

Substituting the values, we get x = [-0.0211 ± √(0.0211² - 4(1)(-0.0211))] / (2(1))

Simplifying further, we get x = [-0.0211 ± √(0.00044521 + 0.084244)] / 2

x = [-0.0211 ± √(0.08468921)] / 2

x = [-0.0211 ± 0.290815] / 2

Therefore, the zeros of the function are approximately x = -0.1479 and x ≈ 0.1689.

The correct answer choice is D) x = -8, x = -2, x = -3.