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Question

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


Solution

Given,
The discriminant of $$3x^{2}+2x+a=0$$ is double the discriminant of $$x^{2}-4x+2=0$$
We know that the discriminant of a quadratic equation $$ax^{2}+bx+c=0$$ is given by: $$b^{2}-4ac$$
Hence,
$$(2)^2-4\times3\times a=2\times((-4)^2-4\times1\times 2)$$
$$4-12a=2\times(16-8)$$
$$4-12a=16$$
$$12a=4-16$$
$$12a=-12$$
$$a=-1$$

Mathematics

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