IIT JEE , AIEEE Forum - Mathematics , Algebra

dixit_se

if the equation ax² + bx + c=0 and x³+3x²+3x+2=0 have two common roots then show that a=b=c

nivedh_89

let m and n b the roots of the quadratic equation............
so for cubis equation,

m+n+3rd root say i = -3
mn+mi+ni = 3
mni = 2..............

m+n = -b/a
mn = c/a

hence i = (b-3a)/a
and i = 2a/c
also i = (c-3a)/b

solve these equations and u will get the required answer......!!!!!!!!!!!

metal

Hey,

x³+3x²+3x+2=(x+2)(x²+x+1)=0 ---------- [eq 1]

Now, if a=b=c; then, ax²+bx+c=0 becomes x²+x+1=0 and so the two roots of this are also those of [eq 1], which satisfies the given condition.

Hence proved.

Tthis was the easiest and shortest way I could find.

rate me if you like my answer.

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