Question

If f(x) = x² - 4x² + 21x – 34 and x– 2 is a factor of f(x), then find all of the

zeros of f(x) algebraically.

Answer 1

To find the zeros of the function f(x), substitute x = 2 into f(x) and solve for zero. Then divide f(x) by x - 2 to find the other zeros.

Step-by-step explanation:

To find the zeros of the function f(x), we need to solve the equation f(x) = 0. Since x - 2 is a factor of f(x), it means that when we substitute x = 2 into f(x), we will get a result of 0.

Substituting x = 2 into f(x) = x² - 4x² + 21x - 34:

f(2) = (2)² - 4(2)² + 21(2) - 34 = 0

Therefore, one of the zeros of f(x) is x = 2.

To find the other zeros, we can use long division or synthetic division to divide f(x) by the factor x - 2. Once we have the quotient, we can set it equal to zero and solve for x. This will give us the other zeros of f(x).