Question

if alpha and beta are the zeroes of the quadratic polynomial 4x²-5x-1,find the value of alpha/ beta +beta/alpha

Answer 1

alpha and beta are roots
sum of roots= -b/a
= -(-5/4)
= 5/4
product of roots= c/a
= -1/4
now,alpha/beta + beta/alpha
=(alpha)² + (beta)²/alpha.beta
=(alpha + beta)² - 2alpha.beta/alpha.beta
=(5/4)² - 2(-1/4)\-1/4
=25/16 - (-1/2)\-1/4
=25+8/16\-1/4
=33/16\-1/4
=33/16*-1/4
= -33/4



hope it'll help u