Question

if alpha and beta are the zeros of the polynomial X square + 2 X + 1 find a quadratic polynomial whose zeros are Alpha square beta and alpha beta square.



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Answer 1

finding the zeros of the polynomial using using factorization
x^2+2x+1
=x^2+x+x+1
=x(x+1)+1(x+1)
=(x+1)(x+1)
therefore the zeros are -1 and -1
a polynomial can be written in the form
k(x^2-x(sum of zeros)+product of zeros
k=constant (k=any number)
substituting values
k(x^2-x(-1+-1)+-1*-1)
=k(x^2+2x+1) is the polynomial