If fix) is divided by (x - a)(x - f ) where \alpha\neq\beta, then what is the remainder ?

Correct Answer is : (x−β)f(α)−(x−α)f(β)α−β

\frac{(x-\alpha) f(\alpha)-(x-\beta) f(\beta)}{\alpha-\beta}

\frac{(x-\alpha) f(\beta)-(x-\beta) f(\alpha)}{\alpha-\beta}

\frac{(x-\beta) f(\alpha)-(x-\alpha) f(\beta)}{\alpha-\beta}

\frac{(x-\beta) f(\beta)-(x-\alpha) f(\alpha)}{\alpha-\beta}

UPSC CDS 1 2020 Math Paper

Question : 22 of 100

Marks: +1, -0

If fix) is divided by (x - a)(x - f ) where α≠β, then what is the remainder ?

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