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Match the following columns for the equation $x^{2} + a | x | + 1 = 0$ where ‘a’ is a parameter.
LIST-I LIST - II
I Roots of $4 x^{2} - 21 x - 25 = 0$ are P 4, 4
II The roots of $3 x^{2} + 4 x + 15 = 0$ are Q 1, 1
III The roots of $2 x^{2} - 4 x + 2 = 0$ are R Imaginary
IV The roots of $x^{2} - 8 x + 16 = 0$ are S $- 1, \frac{25}{4}$
T $1, - \frac{25}{4}$

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$I - R, I I - Q, I I I - S, I V - P$

$I - S, I I - R, I I I - Q, I V - P$

$I - P, I I - R, I I I - Q, I V - T$

$I - R, I I - T, I I I - S, I V - Q$

answer is B.

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Detailed Solution

Let take $| x |^{2} + a | x | + 1 = 0$
I) If $a \geq 0,$ vertex = $(\frac{- a}{2}, \frac{4 - a^{2}}{4})$
Expression is +ve : $∴$ No solution
II) If $a = - 2$
$∴$ Two real solution
III) Three real solution not possible solution
IV) Four real solutions $∴$ $a < - 2$
For example : $a = - 30$

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