If the roots of the quadratic equation x2+px+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 x2+px+q=0 are tan 30°, and tan 15° respectively, then the value of 2 + q - p is : (A) 3 (B) 0 (C) 1 (D) 2

Tardigrade Admin · Accepted Answer

Since tan 30Â° and tan 15Â° are roots of equation x2+px+q=0. ∴ tan 30Â°+tan 15Â°=- p and tan 30Â° tan 15Â°=q Therefore 2+q-p=2+tan 30Â° tan 15Â° +(tan 30Â°) =2+tan 30Â° tan 15Â°+1-tan 30Â° tan 15Â° (∵ tan 45Â°=(tan 30Â°+tan 15Â°/1-tan 30Â° tan 15Â°)) ⇒ 2+q-p=3

Q. If the roots of the quadratic equation $x^{2} + p x + q = 0$ are $t an 3 0^{°}$ , and $t an 1 5^{°}$ respectively, then the value of $2 + q - p$ is :

$3$

$0$

$1$

$2$

Q. If the roots of the quadratic equation x2+px+q=0 are tan30°, and tan15° respectively, then the value of 2+q−p is :

3

0

1

2

Since tan 30° and tan15° are roots of equation x2+px+q=0. ∴tan30°+tan15°=−p and tan30°tan15°=q Therefore 2+q−p=2+tan30°tan15°+(tan30°) =2+tan30°tan15°+1−tan30°tan15° (∵tan45°=1−tan30°tan15°tan30°+tan15°​) ⇒2+q−p=3

Q. If the roots of the quadratic equation $x^{2} + p x + q = 0$ are $t an 3 0^{°}$ , and $t an 1 5^{°}$ respectively, then the value of $2 + q - p$ is :

$3$

$0$

$1$

$2$