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Question 90
For which of the following values of x is the inequality $$x(x+3) < 10$$ satisfied ?
Solution
NOTE :- For an inequality :
case 1 : $$(x - a) (x - b) > 0$$
=> $$x < a $$ & $$ x > b$$ [ if a < b]
case 2 : $$(x - a) (x - b) < 0$$
=> $$a < x < b $$ [ if a < b]
$$x(x + 3) < 10$$
=> $$x^{2} + 3x - 10 < 0$$
=> $$x^{2} + 5x - 2x - 10 < 0$$
=> $$x(x + 5) -2(x + 5) < 0$$
=> $$(x + 5) (x - 2) < 0$$
=> -5 < x < 2 [using case 2]
=> Ans - (B)
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