The values of x satisfying -x-3-x2-4 x-3 is-areA- -1B- 0C- 3D- 6

The correct options are A 1 D 6When x lt; 3 −(x + 3) = x^2 − 4x − 3 ⇒ x^2 − 3x = 0 ⇒ x(x 3)=0 ⇒ x = 0, 3 (Not possible) When x ≥ 3 x + 3 = x^2 − 4x − 3 ⇒ ...

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Standard XII

Mathematics

Absolute Value Function

The values of...

Question

The value(s) of $x$ satisfying $| x + 3 | = x^{2} - 4 x - 3$ is/are

- 1

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0

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3

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6

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Solution

The correct options are
A $- 1$
D $6$
When $x < - 3$
$- (x + 3) = x^{2} - 4 x - 3 \Rightarrow x^{2} - 3 x = 0$
$\Rightarrow x (x - 3) = 0$
$\Rightarrow x = 0, 3 (Not possible)$

When $x \geq - 3$
$x + 3 = x^{2} - 4 x - 3$
$\Rightarrow x^{2} - 5 x - 6 = 0$
$\Rightarrow (x - 6) (x + 1) = 0 \Rightarrow x = 6, - 1$

$∴ x = - 1, 6$

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Absolute Value Function

Standard XII Mathematics

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The value(s) of x satisfying |x+3|=x2−4x−3 is/are

The correct options are A −1 D 6When x<−3 −(x+3)=x2−4x−3⇒x2−3x=0 ⇒x(x−3)=0 ⇒x=0,3 (Not possible) When x≥−3 x+3=x2−4x−3 ⇒x2−5x−6=0 ⇒(x−6)(x+1)=0⇒x=6,−1 ∴x=−1,6

The value(s) of $x$ satisfying $| x + 3 | = x^{2} - 4 x - 3$ is/are