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Common Roots

If px 2+5 x +...

Question

If $p x^{2} + 5 x + 2 = 0$ and $3 x^{2} + 10 x + q = 0$ have both roots in common, then

A

p = 4

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B

q = \frac{3}{2}

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C

p = \frac{3}{2}

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D

q = 4

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Solution

The correct options are
C $p = \frac{3}{2}$
D $q = 4$
Comparing both the equation $p x^{2} + 5 x + 2 = 0$ and $3 x^{2} + 10 x + q = 0$ , we get

$\frac{p}{3} = \frac{5}{10} = \frac{2}{q} \Rightarrow p = \frac{3}{2}, q = 4$

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