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if alpha and beta are the zeroes of the polynomial f(x) = 4x^2-5x+1, find a quadratic polynomial whose zeroes are alpha^2/beta and beta^2/alpha.

if alpha and beta are the zeroes of the polynomial f(x) = 4x^2-5x+1, find a quadratic polynomial whose zeroes are alpha^2/beta and beta^2/alpha.

Grade:10

1 Answers

Pragya Sahu
19 Points
3 years ago
As we know alpha=-b/a and beta =c/a of the eqn of the form ax+by+c=0Now, we have 4x^2-5x+1=0we get alpha=5/4 and beta=1/4According to question,the zeroes are x=alpha^2/beta and x= beta^2/alphaor x-alpha^2/beta=0and x-beta^2/alpha=0(x-alpha^2/beta)(x-beta^2/alpha)=0On solving we have,alpha.beta.x^2-x(alpha^3+beta^3)+alpha^2.beta^2=0Putting the value of alpha and beta in this eqn,we have80x^2-504x+25=0

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