Question

Obtain all other zeroes of polynomial p(x) = 2x^4- 2x^3 - 7x^2 +3x +6, if two of its zeroes are √3÷2 and √–3÷2

Answer 1

Given,

f(x)= 2x4 – 2x3 – 7x2 + 3x + 6

Since, two of the zeroes of polynomial are −√(3/2) and √(3/2) so, (x + √(3/2)) and (x –√(3/2)) are factors of f(x).

⇒ x2 – (3/2) is a factor of f(x). Hence, performing division algorithm, we get

⇒ f(x)= (2x2 – 2x – 4)( x2 – 3/2)

= 2(x2 – x – 2)( x2 – 3/2)

So, putting x2 – x – 2 = 0 we can get the other 2 zeros. ⇒

(x – 2)(x + 1) = 0

∴ x = 2 or -1

Hence, all the zeros of the polynomial are −√(3/2), -1, √(3/2) and 2