Question

If alpha and beta are the zeros of the quadratic polynomial X square +2x+1,then find the quadratic polynomial whose zeros are alpha square beta and alpha beta square.

Answer 1

Final Answer :
${x}^{2} + 2x + 1 = 0$
Steps:
1)
General Method :
If α and β are are zeroes of the quadratic polynomial x^2+2x+1 =0 .
Here,
αβ = 1
So,
α^2β = α * (αβ) = α * 1 = α
αβ^2 = (αβ)*β = β

2) Now, here we see that
Quadratic polynomial whose zeroes are α^2β and αβ^2 is same as quadratic polynomial whose zeroes are. α and β ,.
I. e
${x}^{2} + 2x + 1$