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If the equation that formed by squaring each root of the equation $5 x^{2} + 2 x - 7 = 0$ is $a x^{2} + b x + c = 0,$ then among the following incorrect statement is

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$a = 25$

$b = - 74$

$a + b + c = 5$

$c = 49$

answer is C.

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Detailed Solution

$f (\sqrt{x}) = 0 \Rightarrow 5 {(\sqrt{x})}^{2} + 2 (\sqrt{x}) - 7 = 0$

$5 x + 2 \sqrt{x} - 7 = 0$

$\begin{array}{l} 5 x - 7 = - 2 \sqrt{x} \\ {(5 x - 7)}^{2} = {(- 2 \sqrt{x})}^{2} \\ 25 x^{2} + 49 - 70 x = 4 x \\ 25 x^{2} - 70 x + 49 - 4 x = 0 \\ 25 x^{2} - 70 x - 4 x + 49 = 0 \\ 25 x^{2} - 74 x + 49 = 0 \end{array}$

comparing $a x^{2} + b x + c = 0$

$a = 25$ $b = - 74$ $c = 49$

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