Question

Obtain all zeroes of 3x 4 15x 3 + 13x 2 + 25x 30 , if two of its zeroes are 5 3 and 5 3

Answer 1

Answer:

p(x) = 3x^4 – 15x^3 + 13x^2+ 25x – 30

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

⇒ x2 - 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