If a polynomial 4x⁴-4x³-35x²+36x-9 has two zeroes 3 and -3 , then find the other zeroes
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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
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