Let $tan α, tan β$ be the roots of the quadratic equation $x^{2} - 3 x - 1 = 0$ then the value of $tan (α + β)$ is

0

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\frac{3}{2}

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\frac{2}{3}

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none of these

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Solution

The correct option is B $\frac{3}{2}$
Given $tan α, tan β$ be the roots of the equation $x^{2} - 3 x - 1 = 0$ .
Then from the relation between the roots and co-efficients we get,
$tan α + tan β = 3$ .....(1) and $tan α . tan β = - 1$ .....(1).
Now
$tan (α + β)$
$= \frac{tan α + tan β}{1 - tan α . tan β}$
$= \frac{3}{1 - (- 1)}$ [ Using (1) and (2)]
$= \frac{3}{2}$ .

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Let tanα,tanβ be the roots of the quadratic equation x2−3x−1=0 then the value of tan(α+β) is

The correct option is B 32Given tanα,tanβ be the roots of the equation x2−3x−1=0.Then from the relation between the roots and co-efficients we get, tanα+tanβ=3.....(1) and tanα.tanβ=−1.....(1).Now tan(α+β)=tanα+tanβ1−tanα.tanβ=31−(−1) [ Using (1) and (2)]=32.

Let $tan α, tan β$ be the roots of the quadratic equation $x^{2} - 3 x - 1 = 0$ then the value of $tan (α + β)$ is