Question

If alpha and beta are the zeros of polynomial f(x) = x^2-x-6, find a polynomial whose zeros are alpha^2/beta^2 and beta^2/alpha^2

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

$x {}^{2} - x - 6 = 0$

$x {}^{2} - 3x + 2x - 6 = 0$

$x(x - 3) + 2(x - 3) = 0$

$x = 3 \: or \: x = - 2$

$let \: \alpha = 3 \: \: \: \: \: \: \: \: \: \: \beta = - 2$

$\alpha {}^{2} \div \beta {}^{2} = 3 { }^{2} \div (- 2) {}^{2} = 9 \div 4$

$\beta {}^{2} \div \alpha {}^{2} = (- 2) {}^{2} \div( 3 {}^{2} ) = 4 \div 9$