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Q.

$2 x^{2} + x - 1 \leq 0 \Rightarrow x$ belongs to the interval

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a

$3 \leq x \leq 4$

b

$- 1 \leq x \leq \frac{1}{2}$

c

$2 \leq x \leq \frac{1}{3}$

d

$1 \leq x \leq \frac{1}{2}$

answer is A.

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Detailed Solution

$2 x^{2} + x - 1 \leq 0$

$2 x^{2} + 2 x - x - 1 \leq 0$

$2 x (x + 1) - 1 (x + 1) \leq 0$

$(2 x - 1) (x + 1) \leq 0$

$- 1 \leq x \leq \frac{1}{2}$

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2x2+x−1≤0⇒x belongs to the interval