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Inequalities Involving Mathematical Means

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 common, then 2r-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 equation can be written as

$(6 k + 2) x^{2} + r x + 3 k - 1 = 0$ .......(i)

and $2 (6 k + 2) x^{2} + p x + 2 (3 k - 1) = 0$ ......(ii)

Condition for common roots is

$\frac{12 k + 4}{6 k + 2} = \frac{p}{r} = \frac{6 k - 2}{3 k - 1} = 2 o r 2 r - p = 0$

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