Obtain all zeroes of 3x^{4} – 15x^{3} + 13x^{2} + 25x – 30, if two of its zeroes are √5/3 and – √5/3

### Answer

p(x) = 3x^{4} – 15x^{3} + 13x^{2} + 25x – 30

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

⇒ x^{2} - 5/3 or (3x^{2} - 5)/3 is a factor of p(x)

p(x) = (3x^{2} - 5)/3 × (x^{2} – 5x + 6)

= 1/3 × (3x^{2} – 5) (x – 3) (x – 2)

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