Common Roots

Quadratic equation of Class 11

Common Roots

Suppose the quadratic equations ax2 + bx + c =0 and a′x2 + b′x + c′ = 0 a, (a′ ≠ 0 and ab′ - a′ b ≠ 0) have a common root.

Let this common root be α. Then aα2 + bα + c = 0 and a′α2 + b′α + c′ = 0

On solving by using Cramer's Rule.

We get Common Roots

Eliminating α we get (bc′-b′c) (ab′-a′b) = (a′c-ac′)2 giving us the condition for one root to be common. However, if ab′-a′b = 0 then giving both the roots common.

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