Which of the following ranges of x satisfies the quadratic inequality 2x^2 - 7x + 3 < 0? — JAMB UTME

Which of the following ranges of $x$ satisfies the quadratic inequality $2x^2 - 7x + 3 < 0$ ?

\frac{1}{2} < x < 3

Factorizing

2x^2 - 7x + 3 < 0

gives

(2x - 1)(x - 3) < 0

. The roots of the quadratic equation

(2x - 1)(x - 3) = 0

are

x = \frac{1}{2}

and

x = 3

. Because the coefficient of

x^2

is positive, the quadratic curve opens upwards and is strictly negative between the two roots. Therefore, the inequality is satisfied when

\frac{1}{2} < x < 3

Factorize the quadratic expression

2x^2 - 7x + 3 = (2x - 1)(x - 3)

Factorization allows us to find the critical values of the inequality.

Determine the critical values by setting the factored expression to zero

x = \frac{1}{2}

and

x = 3

These points mark the boundary values where the quadratic expression changes sign.

Test intervals or apply sign analysis for strict inequality

< 0

The product

(2x - 1)(x - 3)

is negative for

\frac{1}{2} < x < 3

Since the leading coefficient is positive (

2 > 0

), the parabola opens upwards and takes negative values strictly between its real roots.

Solving Quadratic Inequalities by Factorization and Interval Sign Analysis

Estimated Time:1m 15s

Question