Question

14).If a polynomial 4x4 - 4x3 – 35x2 + 36x – 9 has two zeroes as 3
and -3, find the other zeroes.​

Answer 1

• Given 2 roots are 3,-3
• let the given polynomial be p(x)
• now we know that x=3,-3 or x+3=0 and x-3=0
• to find the other 2 roots we have to divide p(x) by [(x+3)(x-3)] and equate the result to zero
• [(x+3)(x-3)] is equal to x^2 - 9
• solving p(x)÷(x^2 - 9) guves a quadratic 4x^2 - 4x + 1
• this is a perfect square of (2x-1)^2
• and hence equating it to zero gives x=1/2,1/2