Let the rootsnof ax^2+bx+c=0 be r and s. The equation with roots ar+b and as+b is
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r+s=-b/a
rs=c/a
now given ar+b, as+b
ar+b+as+b=sum of roots
a (r+s)+2b=sum of roots
a. (-b/a)+2b=b
and product of roots=(ar+b)(as+b)=a^2rs+arb+bas+b^2
=a^2.c/a+ab (-b/a)+b^2=ac
now equation
x^2-(sum of roots) x+product of roots
x^2-bx+ac is answer
rs=c/a
now given ar+b, as+b
ar+b+as+b=sum of roots
a (r+s)+2b=sum of roots
a. (-b/a)+2b=b
and product of roots=(ar+b)(as+b)=a^2rs+arb+bas+b^2
=a^2.c/a+ab (-b/a)+b^2=ac
now equation
x^2-(sum of roots) x+product of roots
x^2-bx+ac is answer
abhi178:
m^2+n^2+2mn=1+4mn
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