# If the root of the equation x^2+px+q =0 are tan 30 degree and tan 15 degree, then the value of 2+q-p is

Solution:We have , $x^2+px-p=0$

$tan30^{\circ}+tan15^{\circ}=-p;and; tan30^{\circ}\times tan15^{\circ}=-q$

$\\45^{\circ}=30^{\circ}+15^{\circ}$

Taking tan both side we get ,

$\\ tan45^{\circ}=tan(30^{\circ}+15^{\circ})\\ \\\Rightarrow tan30^{\circ}+tan15^{\circ}/1-tan30^{\circ}tan15^{\circ}=-p/1+q=1\\ \\\Rightarrow -p=1-q\\ \\\Rightarrow 2+q-p=3$

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