Question

Find all the zeroes of the polynomial x⁴ + x³ – 34x² – 4x + 120, if the two of its zeros are 2 and -2.

Answer 1

Let,

f(x) = x⁴ + x³ – 34x² – 4x + 120 

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

⇒ x² – 4 is a factor of f(x). Hence, performing division algorithm, we get

⇒ f(x)= (x² + x – 30)( x² – 4) 

So, putting x² + x – 30 = 0 we can get the other 2 zeros. 

⇒ (x – 6)(x + 5) = 0 

∴ x = 6 or -5 

Hence, all the zeros of the polynomial are -5, -2, 2 and 6.