How many integer values of x satisfy the quadratic inequality 2x^2 - 7x - 4 \le 0? — JAMB UTME

How many integer values of $x$ satisfy the quadratic inequality $2x^2 - 7x - 4 \le 0$ ?

Answer: 5

There are 5 integer values of x that satisfy the inequality.

Solving the quadratic inequality yields

-\frac{1}{2} \le x \le 4

. The integer solutions within this interval are

0, 1, 2, 3,

and

4

. Counting them gives a total of

5

valid integer values.

Factor the quadratic expression.

(2x + 1)(x - 4) \le 0

Factoring allows determination of the critical boundary points.

Find the critical values (roots of the equation).

x = -\frac{1}{2}

and

x = 4

The roots divide the number line into test intervals.

Determine the solution set of the inequality.

-\frac{1}{2} \le x \le 4

Since the quadratic coefficient is positive, the quadratic expression is non-positive between its roots.

List and count the integers within the range.

The integers are

0, 1, 2, 3, 4

, making a total of

5

integers.

Counting only whole numbers in the closed interval

[ -0.5, 4 ]

Quadratic Inequalities and Integer Solution Counting

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