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Absolute Value Function

If |x2+5x-6|=...

Question

If $| x^{2} + 5 x - 6 | = 6 - 5 x - x^{2}$ , then $x \in$

[- 6, 1]

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(- 6, 1)

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(- 6, 1]

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[- 6, 1)

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Solution

The correct option is A $[- 6, 1]$
$| x^{2} + 5 x - 6 | = 6 - 5 x - x^{2}$
$\Rightarrow x^{2} + 5 x - 6 \leq 0$
$\Rightarrow (x + 6) (x - 1) \leq 0$
$\Rightarrow - 6 \leq x \leq 1$
$∴ x \in [- 6, 1]$

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:

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

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

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

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

f (x) = 5 x - x^{2}

f (x) = 6

x =

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