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If \( f(x)=x^{2}-3 x \) and \( \alpha, \beta \) are the roots of the equation \( f(x)=f^{\prime}(x) \), then \( \alpha+\beta \) is (a) 5 (b) -5 (c) 3 (d) -3 |
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Answer» Correct option is (a) 5 \(f(x) = x^2 - 3x\) \(\therefore f' (x) = 2x - 3\) \(f(x) = f'(x)\) ⇒ \(x^2 - 3x = 2x - 3\) ⇒ \(x^2 - 5x + 3 = 0\) ......(1) Given that α & ß are roots of the equation f(x) = f'(x), it means α & ß are roots of equation( 1). \(\therefore\) Sum of roots = α + ß = \(\frac{-(-5)}1\) = 5. |
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