A quadratic equation $x^{2} - 4 | x | - 12 = 0$ represents a curve in $x - y$ plane. if a line $y = k$ passes through the curve and have four different solutions then value of $k$ may be:

- 16 < k < - 12

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- 16 < k < - 6

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- 12 < k < 16

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None of these

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Solution

The correct option is C $- 16 < k < - 12$
The equation of given curve is $x^{2} - 4 | x | - 12 = 0$
$\Rightarrow (| x | - 6) (| x | + 2) = 0$
The graph of above function is shown here.
$y = k$ is a line parallel to $x$ axis.
So we get $4$ solutions if $- 16 < k < - 12$ .
Therefore correct option is $A$ .

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A quadratic equation x2−4|x|−12=0 represents a curve in x−y plane. if a line y=k passes through the curve and have four different solutions then value of k may be:

The correct option is C −16<k<−12The equation of given curve is x2−4|x|−12=0⇒(|x|−6)(|x|+2)=0The graph of above function is shown here.y=k is a line parallel to x axis.So we get 4 solutions if −16<k<−12.Therefore correct option is A.

A quadratic equation $x^{2} - 4 | x | - 12 = 0$ represents a curve in $x - y$ plane. if a line $y = k$ passes through the curve and have four different solutions then value of $k$ may be: