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#