Q58 / 150 · JEE Main 2006 · Mathematics

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

  • A
    2
  • Correct answer
    B
    3
  • C
    0
  • D
    1

Solution

$x^2+p x+q=0$ $\tan 30^{\circ}+\tan 15^{\circ}=-p$ $\tan 30^{\circ} \cdot \tan 15^{\circ}=q$ $\tan 45^{\circ}=\frac{\tan 30^{\circ}+\tan 15^{\circ}}{1-\tan 30^{\circ} \tan 15^{\circ}}=\frac{-p}{1-q}=1$ $\Rightarrow-p=1-q$ $\Rightarrow q-p=1 \quad \therefore 2+q-p=3$.

Hence, the correct answer is option: 'B'.

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