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Quadratic Equations with Both Roots Common

If both the r...

Question

If both the roots of
$k (6 x^{2} + 3) + r x + 2 x^{2} - 1 = 0$ and
$2 (6 k + 2) x^{2} + p x + 2 (3 k - 1) = 0$
are same, then $2 r - p$ is equal to

A

-1

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B

0

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C

1

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D

2

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Solution

The correct option is B
0

Given equations can be written as
$k (6 x^{2} + 3) + r x + 2 x^{2} - 1 = 0 . . . (i)$ and
$2 (6 k + 2) x^{2} + p x + 2 (3 k - 1) = 0 . . . (i i)$

Condition for common roots is that the corresponding coefficients must be proportional.
$\Rightarrow \frac{12 k + 4}{6 k + 2} = \frac{p}{r}$
$\Rightarrow \frac{6 k - 2}{3 k - 1} = 2$
$\Rightarrow 2 r - p = 0$

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Similar questions

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Q. If the equation

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Q. lf the equations

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