Question

Testing Potential Roots with Substitution

Select all of the following that are potential roots of
p(x)=x4-9x² - 4x +12?
0
+9
n +6

Answer 1

To test potential roots of the polynomial p(x) = x^4 - 9x^2 - 4x + 12, substitute the values 0, 9, and -6 for x. Only x = -6 is a potential root.

Step-by-step explanation:

To test potential roots of the polynomial p(x) = x^4 - 9x^2 - 4x + 12, we substitute the values 0, 9, and -6 for x. We evaluate the polynomial at each value to check if it equals zero. If it does, the corresponding value is a potential root.

1. Testing with x = 0: p(0) = (0)^4 - 9(0)^2 - 4(0) + 12 = 12 (not equal to zero)
2. Testing with x = 9: p(9) = (9)^4 - 9(9)^2 - 4(9) + 12 = 3024 (not equal to zero)
3. Testing with x = -6: p(-6) = (-6)^4 - 9(-6)^2 - 4(-6) + 12 = 0 (equal to zero)

Based on the test, the potential root of the polynomial is x = -6.

Learn more about Finding potential roots of a polynomial using substitution