Solve the polynomial inequality and graph the solution set o

Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation. 2x^2 + 7x

The given inequality is

2 x ² + 7 x < -5, or, 2 x ² + 7 x + 5 < 0

After factorizing the expression we get,

2 x ² + 7 x + 5 < 0, or 2 x ² + 2 x + 5 x + 5 < 0 or 2x(x+1)+5(x+1) < 0

or, (x + 1) (2x + 5) < 0 ... ... (1)

The expression (1) holds only if (x +1) > 0 and ( (2x + 5) < 0 OR (x + 1) < 0 and (2x + 5) > 0.

i.e. x > (-1) and x < (-5/2) OR x < (-1) and x > (-5/2).

i.e. NULL SET OR (-5/2) < x < (-1)

Thus, the solution set is (-5/2) < x < (-1).

OPTION (A). The solution set is (-5/2) < x < (-1).

Depending on the result the correct graph is (A).