Find the value of $2 a^{2} - a + 7,$ if $x^{4} + 2 a x^{2} - 9 = 15$ when $x = 2$ .

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Solution

The correct option is A 8
Given $x^{4} + 2 a x^{2} - 9 = 15$ at $x = 2$ .

let's first put the value of $x = 2$ in the above equation.

$2^{4} + 2 a \times 2^{2} - 9 = 15 ⟹ 16 + 8 a - 9 = 15 ⟹ 8 a + 7 = 15 ⟹ 8 a = 8 ⟹ a = 1$

Now we have to find the value of $2 a^{2} - a + 7$ .
We already calculated value of $a = 1$ .
$⟹ 2 \times 1^{2} - 1 + 7 ⟹ 2 - 1 + 7 = 8$

Hence, option 'a' is correct.

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