Question

Find a quadratic polynomial whose one zero is root 5 and the product of its zeroes is -2 root 5.

Answer 1

$x = 5 \\ \alpha \beta = - 2 \sqrt{5} \\ \alpha \beta = - 2 \sqrt{5} \\ 5 \beta = - 2 \sqrt{5} \\ \beta = - 2 \div \sqrt{5} = - 2 \sqrt{5} \div 5 \\ p(x) = {x}^{2} - ( \alpha + \beta ) + \alpha \beta = 0 \\ p(x) = {x}^{2} + (2 \sqrt{5} - 25)x - 2\sqrt{5} = 0$

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