Question

Obtaine all other zeros of the polynomial 9 x power 4 minus 6 x cube minus 35 X square + 24 x minus 4 if two of its zeros are 2 and -2​

Answer 1

all other zeros of the polynomial 9 x power 4 minus 6 x cube minus 35 X square + 24 x minus 4 if two of its zeros are 2 and -2​,  the other roots are 1/3 and 1/3.

• Given,
• polynomial  = 9x^4 - 6x^3 - 35x^2 + 24x - 4
• two roots  = 2, -2
• ⇒ (x-2) (x+2)
• ⇒ x^2 - 2^2 = x^2 - 4
• we need to divide the polynomial (9x^4 - 6x^3 - 35x^2 + 24x - 4) by (x^2 - 4) in order to obtain other 2 zeros.

• (x^2 - 4) ] 9x^4 - 6x^3 - 35x^2 + 24x - 4 [ 9x^2 - 6x + 1
•                9x^4 -   36x^2
•               -------------------------------------------
•               -6x^3 + x^2 + 24x
•               -6x^3 + 24x
•                -------------------------------------------
•                x^2 - 4
•                x^2 - 4
•               -------------------------------------------
•                0

• (9x^2 + 1 - 6x) is a perfect square of (3x-1)
• Therefore, the roots are 1/3, 1/3