Question

# If the roots of the quadratic equation x2+px+q=0 are tan30o and tan15o then the value of 2 + q - p is

A

1

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B

2

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C

3

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D

4

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Solution

## The correct option is C 3 We know tan(30 + 15) = tan30+tan151−tan30tan15. The value on the LHS is 1 and the RHS can be calculated becuase numerator is sum of the roots and denominator is related to the product of the roots. tan 30, tan 15 are the roots of the equation x2+px+q=0 ⇒tan30+tan15=−p tan 30 + tan 15 = q tan (30 + 15) = tan30+tan151−tan30tan15 tan 45 = −p1−q ⇒ 1-q = -p ⇒q-p = 1 ⇒ 2+q-p = 2+1 = 3

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