MathsGee is Zero-Rated (You do not need data to access) on: Telkom |Dimension Data | Rain | MWEB

0 like 0 dislike
15 views
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

1) 2
2) 3
3) 0
4) 1
| 15 views

0 like 0 dislike

(2)

Explanation

$x^{2}+p x+q=0$

$\tan 30^{\circ}+\tan 15^{0}=-p$

$\tan 30^{\circ} \cdot \tan 15^{0}=q$

$\tan 45^{\circ}=\frac{\tan 30^{\circ}+\tan 15^{\circ}}{1-\tan 30^{0} \tan 15^{\circ}}=\frac{-p}{1-q}=1$

$\Rightarrow-p=1-q$

$\Rightarrow q-p=1 \quad \therefore 2+q-p=3$

by Bronze Status (9,486 points)

0 like 0 dislike