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Question

If the roots of the quadratic equation x2+px+q=0 are tan30o and tan15o respectively 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
0
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Solution

The correct option is C 3
Roots of x2+px+q=0 are tan30o and tan15o

Sum of roots =p=tan30o+tan15o

Product of roots =q=tan30o.tan15o

tan(30o+15o)=tan30o+tan15o1tan30otan15o=p1q

tan(45o)=1=p1q

1q+p=0

p+q1=0

Adding 3 on both sides

p+q1+3=3

2+qp=3

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