If the roots of the quadratic equation x2 - px - q - 0 are tan 30- and tan 15- respectively- then value of 2 - q - p is

X^2 + px + q = 0 Sum of roots = tan 30^∘ + tan 15^∘ = p Product of roots = tan 30^∘. tan 15^∘ = q tan 45^∘ = tan 30^∘ + tan 15^∘/1 tan 30^∘. tan 15^∘ = p/1 q ...

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Byju's Answer

Standard XIII

Mathematics

Relation between Roots and Coefficients for Quadratic

If the roots ...

Question

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

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Solution

The correct option is B 3
$x^{2} + p x + q = 0$
Sum of roots = tan $30^{\circ} + t a n 15^{\circ} = - p$
Product of roots = $t a n 30^{\circ} . t a n 15^{\circ} = q$
$t a n 45^{\circ} = \frac{t a n 30^{\circ} + t a n 15^{\circ}}{1 - t a n 30^{\circ} . t a n 15^{\circ}} = \frac{- p}{1 - q} = 1 \Rightarrow - p = 1 - q \Rightarrow q - p = 1 ∴ 2 + q - p = 3$

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If the roots of the quadratic equation x2+px+q=0 are tan 30∘ and tan 15∘, respectively, then value of 2 + q - p is

The correct option is B 3x2+px+q=0 Sum of roots = tan 30∘+tan 15∘=−p Product of roots = tan 30∘.tan 15∘=q tan 45∘=tan 30∘+tan 15∘1−tan 30∘.tan 15∘=−p1−q=1⇒−p=1−q⇒q−p=1∴2+q−p=3

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