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Properties of Inverse Function

If fx=4x2+3...

Question

If $f (x) = 4 x^{2} + 3 x - 7$ and $α$ is a common root of the equation $x^{2} - 3 x + 2 = 0$ and $x^{2} + 2 x - 3 = 0$ then the value of $f (α)$ is-

0

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Solution

The correct option is B $0$
$x^{2} - 3 x + 2 = 0 (x - 2) (x - 1) = 0 x = 1 o r 2 x^{2} + 2 x - 3 = 0 (x - 1) (x + 3) = 0 x = 1 o r - 3 ∴ c o m m o n r o o t i s x = 1 f (x) = 4 x^{2} + 3 x - 7 f (1) = 4 + 3 - 7 = 0$

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