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if-in-a-quadratic-eqution-x-2-ax-b-0-and-x-2-bx-a-0-have-a-common-root-then-the-numerical-value-of-a-b-is-

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Question Number 25187 by lucky singh last updated on 05/Dec/17
if in a quadratic eqution x^2 +ax+b=0 and x^2 +bx+a=0 have a common root then the numerical value of (a+b) is
ifinaquadraticequtionx2+ax+b=0andx2+bx+a=0haveacommonrootthenthenumericalvalueof(a+b)is
Commented by prakash jain last updated on 05/Dec/17
let α be a common root α^2 +aα+b=0 (i) α^2 +bα+a=0 (ii) (i)−(ii) (a−b)α+b−a=0 ⇒α=1 put x=1 in x^2 +ax+b=0 a+b=−1
letαbeacommonrootα2+aα+b=0(i)α2+bα+a=0(ii)(i)−(ii)(a−b)α+b−a=0⇒α=1putx=1inx2+ax+b=0a+b=−1

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