Question

If alpha and beta are the two zero of polynomial 6x2+x-1 then find a polynomial who's zero are alpha3beta and beta3alpha​

Answer 1

alpha & beta are the two zero of polynomial 6x^2+x-1=0

therefore, alpha + beta = -1/6 &

alpha × beta = -1/6 ---------- (1)

Given that, alpha3beta & beta3alpha are roots of another polynomial

therefore, alpha3beta + beta3alpha

= alpha × beta (3+3)

= -1/6 (6) ----------- from (1)

= -1

&

alpha3beta × beta3alpha

= (alpha)^2 × (beta)^2 × 3 × 3

= (alpha beta)^2 × 9

= (-1/6)^2 × 9

= (1/36) × 9

= 1/4

therefore, equation is ----

x^2 - (alpha3beta + beta3alpha) × x + (alpha3beta × beta3alpha) = 0

x^2 - (-1)x + (1/4) = 0

x^2 + x + (1/4) = 0

4x^2 + 4x + 1 = 0