Question

if alpha and beta are zeros of p(x)=5x²+4x-9 then find the value of alpha³-beta³

Answer 1

here we will factorize p(x) and then by getting alpha and beta we will substitute their values and then we got the answer as - 854/125

Answer 2

5x^2 + 4x - 9
by middle splitting method
5x^2 + 9x - 5x -9
x(5x + 9) -1(5x + 9)
(x-1)(5x-9)
alpha and beta r the zeroes
so, x-1 = 0
x= 1 (alpha)
and 5x + 9 = 0
x= -9/5 (beta)
now, (alpha)^3 = 1
(beta)^3 = -125/729

(alpha)^3 - (beta)^3 =1 - (-125/729)
=1 + 125/729
=729+125/729
=854/729

hope it helps

byee