If the roots of the quadratic equation `x^2+p x+q=0` are `tan30^0a n dtan15^0,` respectively, then find the value of `2+q-pdot`

Options

A. 2
B. 3
C. 0
D. 1

Answer

B

Explanation

`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`