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Question

If the roots of the quadratic equation x2+px+q=0 are tan 30 and tan 15, respectively, then the value of 2+qp is :

A
2
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B
3
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C
1
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Solution

The correct option is B 3

x2+px+q=0 has roots tan 30 tan 15.
tan 30+tan 15=p.....(1)
and tan 30 tan 15=q......(2)
Now tan 45=tan(30+15)
1=tan 30+tan 151tan 30 tan 15
1=p1q [Using(1) and (2)]
1q=pqp=1
2+qp=3


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