If tan- -tan- are the roots of the equation x2 - px - q - 0 p 0 then

The correct option is D tan( α + β) = p/(q 1) x^2+px+2=0 tanα and tanβ are roots of equation tanα +tanβ = p tanαtanβ =q ...

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Standard XII

Mathematics

Relation between Roots and Coefficients for Quadratic

If tanα ,ta...

Question

If $tan α, t a n β$ are the roots of the equation $x^{2} + p x + q = 0 (p \neq 0)$ then

cos (α + β) = 1 - q

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sin (α + β) = - p

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tan (α + β) = \frac{p}{(q - 1)}

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Solution

The correct option is D $tan (α + β) = \frac{p}{(q - 1)}$
$x^{2} + p x + 2 = 0$
$tan α$ and $tan β$ are roots of equation
$tan α + tan β = - p$
$tan α tan β = q$
$tan (α + β) = \frac{tan α + tan β}{1 - tan α tan β} = \frac{- p}{1 - q} = \frac{p}{q - x}$
$tan (α + β) = \frac{p}{q - 1}$ .

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The correct option is D tan(α+β)=p(q−1)x2+px+2=0tanα and tanβ are roots of equationtanα+tanβ=−ptanαtanβ=qtan(α+β)=tanα+tanβ1−tanαtanβ=−p1−q=pq−xtan(α+β)=pq−1.

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