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

Question

If the roots of the quadratic equation $x^{2} + p x + q = 0$ are $\tan 30 °$ and $\tan 15 °$ , respectively, then the value of $2 + q - p$ is

Smart Achievers · Accepted Answer

(2)

$α = \tan 30 °,$ $β = \tan 15 ° are roots of the equation$ $x^{2} + p x + q = 0$ .

$∴$ $α + β = - p$ and $α β = q$

Using $\tan A + \tan B = \tan (A + B) (1 - \tan A \tan B)$

$\Rightarrow - p = 1 - q \Rightarrow q - p = 1$

$\Rightarrow 2 + q - p = 3$

Want Us to Email you About Special Offers & Updates?