Question

What are the zeros of the polynomial function f(x)=x3-7x2+8x+16

Answer 1

Answer: x=4, -1

Step-by-step explanation:

Assuming you meant $x^3-7x^2+8x+16$, the zeros of the question are x = 4 and -1.

Step 1. Replace f(x) with y.

$y = x^3-7x^2+8x+16$

Step 2. To find the roots of the equation, replace y with 0 and solve.

$0 = x^3-7x^2+8x+16$

Step 3. Factor the left side of the equation.

$(x-4)^2 (x+1)=0$

Step 4. Set x-4 equal to 0 and solve for x.

$x-4=0$

Step 5. Set $x+1$ equal to 0 and solve for x.

$x=-1$

The solution is the result of $x-4=0$ and $x+1=0$.

$x=4,-1$