Form the quadratic equation whose roots $alpha$ and $beta$ satisfy the relations $alpha beta=768$ and $alpha^2+beta^2=1600$ ?

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Answer 1 · 2018-01-06T09:54:40

$x^2-56x+768=0$

if $alpha " and " beta$ are the roots of a quadratic eqn , the eqn can be written as

$x^2-(alpha+beta)x+alphabeta=0$

we are given

$color(red)(alpha beta=768)$

$color(blue)(alpha^2+beta^2=1600)$

now
$(alpha+beta)^2=color(blue)(alpha^2+beta^2)+color(red)(2alphabeta)$

so $(alpha+beta)^2=color(blue)(1600)+2xxcolor(red)(768)=3136$

$:.alpha+beta=sqrt(3136)=56$

the required quadratic is then

$x^2-56x+768=0$

Form the quadratic equation whose roots alphaalpha and betabeta satisfy the relations alpha beta=768alpha beta=768 and alpha^2+beta^2=1600alpha^2+beta^2=1600?