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JEE Main 2006
Exam
JEE Main
Year
2006
Subject
Mathematics
Chapter
Quadratic Equation

JEE Main 2006 · Mathematics · Quadratic Equation

If the roots of the quadratic equation x^2+p x+q=0 are 30^ and 15^...

If the roots of the quadratic equation x2+px+q=0x^2+p x+q=0 are tan⁡30∘\tan 30^{\circ} and tan⁡15∘\tan 15^{\circ}, respectively then the value of 2+q−p2+q-p is

Options

  1. A2
  2. B3
  3. C0
  4. D1

Correct answer

B. 3

Step-by-step solution

x2+px+q=0x^2+p x+q=0 tan⁡30∘+tan⁡15∘=−p\tan 30^{\circ}+\tan 15^{\circ}=-p tan⁡30∘⋅tan⁡15∘=q\tan 30^{\circ} \cdot \tan 15^{\circ}=q tan⁡45∘=tan⁡30∘+tan⁡15∘1−tan⁡30∘tan⁡15∘=−p1−q=1\tan 45^{\circ}=\frac{\tan 30^{\circ}+\tan 15^{\circ}}{1-\tan 30^{\circ} \tan 15^{\circ}}=\frac{-p}{1-q}=1 ⇒−p=1−q\Rightarrow-p=1-q ⇒q−p=1∴2+q−p=3\Rightarrow q-p=1 \quad \therefore 2+q-p=3.
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