Polynomials (C10)

Obtain all zeroes of 3x4 – 15x3 + 13x2 + 25x – 30, if two of its zeroes are √5/3 and – √5/3

Answer

p(x) = 3x4 – 15x3 + 13x2 + 25x – 30

x – √5/3 and x + √5/3 are factors of p(x)

⇒ x2 - 5/3 or (3x2 - 5)/3 is a factor of p(x)

p(x) = (3x2 - 5)/3 × (x2 – 5x + 6)

= 1/3 × (3x2 – 5) (x – 3) (x – 2)

∴ Zeroes of p(x) are √5/3, – √5/3, 2 and 3.