Question

construct a quadratic equation with roots p square and q square​

Answer 1

Answer:

hey here is your solution

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Step-by-step explanation:

$so \: for \: a \: certain \: quadratic \: equation \\ let \: its \: two \: roots \: be \: \alpha \: and \: \beta \\ \\ here \: \\ a = p {}^{2} \\ \beta = q {}^{2} \\ \\ so \: applying \\ \alpha + \beta = p {}^{2} + q {}^{2} \\ \\ \alpha \beta = p {}^{2} .q {}^{2}$

$we \: know \: that \\ x {}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ \\ x {}^{2} - (p {}^{2} + q {}^{2} )x + p {}^{2} .q {}^{2} = 0 \\ \\ thus \: then \\ \: required \: quadratic \: equation \: whose \: roots \: are \: \\ p {}^{2} \: \: and \: q {}^{2} \: is \: \\ x {}^{2} - (p {}^{2} + q {}^{2} )x + p {}^{2} .q {}^{2} = 0$