Question

if alpha and beta are the zeros of the polynomial x²+2x+1 then find the quadratic polynomial whose zeros are α²β &αβ²

Answer 1

Answer...

P(x) = x^2 + 2x +1

It is given that alpha and beta are zeros of p(x)

alpha + beta = - b/a
= -2/1 = -2

alpha × beta = c/a
= 1/1 = 1

Therefore , for a new polynomial ,

Sum of zeros = alpha^2 beta + alpha beta^2

= alpha×beta +( alpha+beta )

= 1 + ( -2 )


= -1

Product of zeros = alpha^2 beta × alpha beta^2

= alpha beta ( alphabeta )

= 1 (1) = 1

q(x) = x^2 + ( sum of zeros ) x + ( product of zeros )

q(x) = x^2 -x +1

Answer 2

q(x)=x²-x+1

Hope it helps you madesh

i am Lokendra