Question

Find all the zeroes of the polynomial 9x⁴−6x³−35x+24x−4, if two of its zeroes are 2 and -2.

a) x=1,x=−1
b) x=0,x=2
c) x=2,x=−2
d) x=1,x=−2

Answer 1

To find all the zeroes of the polynomial 9x⁴−6x³−35x+24x−4 when two of its zeroes are 2 and -2, we can use the factor theorem and divide the polynomial by (x - 2) and (x + 2) to find the remaining zeroes.

Step-by-step explanation:

To find all the zeroes of the polynomial 9x⁴−6x³−35x+24x−4 when two of its zeroes are 2 and -2, we can use the factor theorem. Since 2 and -2 are zeroes of the polynomial, (x - 2) and (x + 2) must be factors of the polynomial. We can divide the polynomial by these factors to find the remaining factors and zeroes.

1. Divide the polynomial by (x - 2). The quotient will be 9x³ + 12x² - 11x + 2.
2. Divide the quotient by (x + 2). The quotient will be 9x² - 6x + 1.
3. Solve 9x² - 6x + 1 = 0 using the quadratic formula. The zeroes will be x = 1 and x = -1/3.

Therefore, the zeroes of the polynomial 9x⁴−6x³−35x+24x−4 when two of its zeroes are 2 and -2 are x = 2, x = -2, x = 1, and x = -1/3.