Question

Select all of the following that are potential roots of

p(x) = x⁴ − 9x² − 4x 12?
a. 0
b. ±2
c. ±4
d. ±9
e. ±3
f. ±6
g. ±12

Answer 1

None of the given options are potential roots of the polynomial p(x) = x⁴ − 9x² − 4x + 12.

Step-by-step explanation:

To find the potential roots of the polynomial p(x) = x⁴ − 9x² − 4x + 12, we need to solve for x. We can do this by factoring or using the quadratic formula. Let's use the quadratic formula:

Substituting the values a = 1, b = -4, and c = 12 into the quadratic formula, we get:

x = (-(-4) ± √((-4)² - 4(1)(12))) / (2(1))

Simplifying this equation gives us:

x = (4 ± √(16 - 48)) / 2

Simplifying further:

x = (4 ± √(-32)) / 2

The expression inside the square root is negative, which means the quadratic equation has no real roots. Therefore, none of the given options (a. 0, b. ±2, c. ±4, d. ±9, e. ±3, f. ±6, g. ±12) are potential roots of p(x) = x⁴ − 9x² − 4x + 12.