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

Answer 1

Nathan Axel

#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#

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Answer 2

Eva Adamson

The quadratic equation is ( x^2 - 1600x + 768 = 0 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.