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Location of Roots

The set of va...

Question

The set of values of $k$ for which the equation $(k + 2) x^{2} - 2 k x - k = 0$ has two roots on the number line symmetrically placed about $1$ is

(- \infty, - 2) \cup (1, \infty)

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(1, \infty)

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{0, 2}

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ϕ

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Solution

The correct option is D $ϕ$

$x -$ coordinate of line of symmetry
$= 1$
So,
$- \frac{b}{2 a} = 1$
$\Rightarrow \frac{2 k}{2 (k + 2)} = 1$
$\Rightarrow k = k + 2$
Therefore, no solution exists.

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