Question 62

Which values of x are satisfied by the inequality $$2x^2 + x - 3 < 0$$?

Solution

Expression : $$2x^2 + x - 3 < 0$$

=> $$2x^2-2x+3x-3<0$$

=> $$(2x+3)(x-1)<0$$

Now product of two numbers is negative only if one is positive and other is negative.

Case I : $$(2x+3)>0$$ => $$x>\frac{-3}{2}$$

and $$(x-1)<0$$ => $$x<1$$

$$\therefore$$ $$\frac{-3}{2}<x<1$$

Case II : $$(2x+3)<0$$ => $$x<\frac{-3}{2}$$

and $$(x-1)>0$$ => $$x>1$$, which is not possible.

=> Ans - (A)

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