If - - are the roots of equation 4x2 - -13x - 7 - 0- then the value of - - - is

If $α, β$ are the roots of the quadratic equation $x^{2} + 3 x + 6 = 0$ , then find the equation whose roots are $\frac{1 + α}{1 - α}$ , $\frac{1 + β}{1 - β}$

If $α a n d β$ are the roots of the equation $4 x^{2} + 3 x + 7 = 0$ , then $\frac{1}{α} + \frac{1}{β} =$

Q. If

α

and

β

are roots of the equation

x^{2} + 5 | x | - 6 = 0

then the value of

| {tan}^{- 1} α - {tan}^{- 1} β |

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If α,β are the roots of equation 4x2−√13x−7=0, then the value of α−β is

The correct option is A 5√54As α,β are roots of 4x2−√13x−7=0then α+β=√134,αβ=−74Now, (α−β)2=(α+β)2−4αβ=1316+7=12516⇒α−β=5√54

If $α, β$ are the roots of equation $4 x^{2} - \sqrt{13} x - 7 = 0$ , then the value of $α - β$ is

The correct option is A $\frac{5 \sqrt{5}}{4}$
As $α, β$ are roots of $4 x^{2} - \sqrt{13} x - 7 = 0$
then $α + β = \frac{\sqrt{13}}{4}, α β = \frac{- 7}{4}$
Now, ${(α - β)}^{2} = {(α + β)}^{2} - 4 α β = \frac{13}{16} + 7 = \frac{125}{16}$
$\Rightarrow α - β = \frac{5 \sqrt{5}}{4}$