Question

Solution of $(2x+1)(x−3)(x+7)<0$ is

• A. $\left(−∞,−7\right)∪\left(−\frac{1}{2},3\right)$
• B. $\left(−∞,−7\right)∪\left(\frac{1}{2},3\right)$
• C. $\left(−∞,7\right)∪\left(−\frac{1}{2},3\right)$
• D. $\left(−∞,−7\right)∪\left(3,∞\right)$

Answer 1

Answer: (A)

$\left(2x+1\right)\left(x−3\right)\left(x+7\right)=0$
$⇒x=−\frac{1}{2}$, $3$, $−7$
Figure shows how the sign changes as one passes through the points $−7$, $−\frac{1}{2}$ , $3$.

Clearly $(2x+1)(x−3)(x+7)<0$
when $x<−7$ or $−\frac{1}{2}<x<3$
$∴x∈\left(−∞,−7\right)∪\left(−\frac{1}{2},3\right).$