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If the roots of the quadratic equation x...

If the roots of the quadratic equation `x^(2)+p x+q=0` are tan `30^(circ) and tan 15^(circ)` respectively, then the value of `2+q-p` is

A

2

B

3

C

0

D

1

Text Solution

Verified by Experts

The correct Answer is:
B
`x^(2)+px+q=0`
Sum of the roots `=tan30^(@)+tan15^(@)=-p`
Product of the roots `=tan30^(@).tan 15^(@)=q`
`tan45^(@)=tan(30^(@)+15^(@))=(tan 30^(@)+tan 15^(@))/(1-tan30^(@).tan15^(@))`
`implies1=(-p)/(1-q)implies-p=1-q`
`impliesq-p=1`
`:.2+q-p=3`
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