Question

3. Find all the zeroes of the polynomial x4 + 2x3 - 8x2 - 18x - 9, if two of its zeroes are 3

and -3.​

Answer 1

2b2t

Explanation:

2b2t

Answer 2

x = 3, x = - 3, x = - 1 with multiplicity 2

Explanation:

Given that x = 3 and x = - 3 are zeros then

(x - 3) and (x + 3) are factors and

(x - 3)(x + 3) = x² - 9 ← is a factor

Using long division to divide the polynomial by x² - 9 gives

quotient = x² + 2x + 1 = (x + 1)² and equating to zero

(x + 1)² = 0 ⇒ x + 1 = 0 ⇒ x = - 1 with multiplicity 2

Hence the zeros of the polynomial are

x = 3, x = - 3, x = - 1 with multiplicity 2