If $\frac{1}{α}$ is a root of the equation $2 x^{2} - 5 x + 7 = 0$ , then the value of $7 α^{2} - 5 α$ is

- 2

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Solution

The correct option is A $- 2$
$2 x^{2} - 5 x + 7 = 0$

$\frac{1}{α}$ is root of equation (1) then

$2 \times {\frac{1}{α}}^{2} \frac{- 5}{α} + 7 = 0$

$\Rightarrow \frac{2}{α^{2}} \frac{- 5}{α} + 7 = 0$

$\Rightarrow 2 - 5 α + 7 α^{2} = 0$

$7 α^{2} - 5 α = - 2$

$∴ [7 α^{2} - 5 α = - 2]$

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α

β

x^{2} + 5 x - 7 = 0

\frac{1}{α} a n d \frac{1}{β}

If $α, β$ are the roots of the equation $2 x^{2} + 5 x + 6 = 0$ , then find the equation whose roots are $\frac{1}{α} a n d \frac{1}{β}$ .

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