If the roots of the equation x2-4x8x-6-k-1k-1 are equal in magnitude and opposite in sign- then the value of k is

X^2+4x8x+6=k 1k+1 ⇒ x^2 +4x = (k 1k+1)× (8x+6) ⇒ nbsp;x^2 + (4 8(k 1)k+1)x 6(k 1k+1) = 0 Let the root be l,m l+m=0 (∵ l= m) So, 4 8(k 1)k+1 nbsp;= 0 ...

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Byju's Answer

Standard XII

Mathematics

Discriminant

If the roots ...

Question

If the roots of the equation $\frac{x^{2} + 4 x}{8 x + 6} = \frac{k - 1}{k + 1}$ are equal in magnitude and opposite in sign, then the value of $k$ is

\frac{1}{3}

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Solution

The correct option is C $3$
$\frac{x^{2} + 4 x}{8 x + 6} = \frac{k - 1}{k + 1} \Rightarrow x^{2} + 4 x = (\frac{k - 1}{k + 1}) \times (8 x + 6) \Rightarrow x^{2} + (4 - \frac{8 (k - 1)}{k + 1}) x - 6 (\frac{k - 1}{k + 1}) = 0$

Let the root be $l, m$
$l + m = 0 (∵ l = - m)$
So, $4 - \frac{8 (k - 1)}{k + 1} = 0$
$\Rightarrow k = 3$

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Discriminant

Standard XII Mathematics

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If the roots of the equation x2+4x8x+6=k−1k+1 are equal in magnitude and opposite in sign, then the value of k is

The correct option is C 3x2+4x8x+6=k−1k+1⇒x2+4x=(k−1k+1)×(8x+6)⇒x2+(4−8(k−1)k+1)x−6(k−1k+1)=0 Let the root be l,m l+m=0 (∵l=−m) So, 4−8(k−1)k+1=0 ⇒k=3

If the roots of the equation $\frac{x^{2} + 4 x}{8 x + 6} = \frac{k - 1}{k + 1}$ are equal in magnitude and opposite in sign, then the value of $k$ is