If the discriminant of $3 x^{2} + 2 x + a = 0$ is double the discriminant of $x^{2} - 4 x + 2$ , then find the value of a.

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Solution

Consider the given equations.
$3 x^{2} + 2 x + a = 0$ $. . . . . . . (1)$
$x^{2} - 4 x + 2 = 0$ $. . . . . . . . (2)$

Since, $D_{1} = 2 D_{2}$

Therefore,
$b_{1}^{2} - 4 a_{1} c_{1} = 2 (b_{2}^{2} - 4 a_{2} c_{2})$
$2^{2} - 4 \times 3 \times a = 2 ((- 4)^{2} - 4 \times 1 \times 2)$
$4 - 12 a = 2 (16 - 8)$
$4 - 12 a = 16$
$- 12 a = 12$
$a = - 1$

Hence, this is the answer.

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