Question

The polynomial f(x) given below has -1 as a zero. f(x)=x³−9x²+40x+50 Find the other zeros of f(x). List the zeros separated by a comma.

Answer 1

To find the other zeros of the polynomial f(x) = x³ - 9x² + 40x + 50, we can use synthetic division to divide the polynomial by (x + 1), since -1 is given as a zero. Performing synthetic division, we get: x² - 10x - 50. Next, we can use either factoring or the quadratic formula to solve the quadratic equation x² - 10x - 50 = 0. Factoring this quadratic equation, we get (x - 5)(x - 10) = 0. Therefore, the other zeros of f(x) are 5 and 10.

Step-by-step explanation:

To find the other zeros of the polynomial f(x) = x³ - 9x² + 40x + 50, we can use synthetic division to divide the polynomial by (x + 1), since -1 is given as a zero.

Performing synthetic division, we get: x² - 10x - 50

Next, we can use either factoring or the quadratic formula to solve the quadratic equation x² - 10x - 50 = 0. Factoring this quadratic equation, we get (x - 5)(x - 10) = 0. Therefore, the other zeros of f(x) are 5 and 10.