JAMB UTME Prep•14 Sept 2026• 3 min read

Quadratic Equations for JAMB Mathematics – Full Explanation

Understand quadratic equations for JAMB Mathematics with simple explanations and worked examples — the way they actually show up in JAMB questions.

A quadratic equation is any equation that can be written in the form ax² + bx + c = 0, where a is not zero. Here's exactly how JAMB tests this topic and how to solve it fast.

What Is a Quadratic Equation?

A quadratic equation is an equation where the highest power of the unknown (usually x) is 2. The general form is:

ax² + bx + c = 0

where a, b, and c are numbers, and a cannot be 0 (if a were 0, there'd be no x² term, and it wouldn't be quadratic anymore).

Every quadratic equation has two solutions (called roots), though sometimes both roots are the same value, and sometimes they involve negative numbers under a square root (which JAMB rarely tests at that level).

How JAMB Tests This

JAMB Mathematics typically tests quadratic equations in three ways:

Solve for x — given an equation, find both values of x
Sum and product of roots — given the equation, find the sum or product of the two roots without fully solving
Form the equation — given the roots, work backward to write the original equation

There are three main methods to solve a quadratic equation: factorization, completing the square, and the quadratic formula. JAMB usually rewards factorization when the equation factors neatly, since it's the fastest method under exam time pressure.

Worked Example 1: Solving by Factorization

Solve: x² + 5x + 6 = 0

Step 1: Find two numbers that multiply to give 6 (the c value) and add to give 5 (the b value). Those numbers are 2 and 3, because 2 × 3 = 6 and 2 + 3 = 5.

Step 2: Rewrite the equation using these numbers: (x + 2)(x + 3) = 0

Step 3: Since the product of two things is 0, at least one of them must be 0: x + 2 = 0 → x = -2 x + 3 = 0 → x = -3

Answer: x = -2 or x = -3

Worked Example 2: Sum and Product of Roots

Find the sum and product of the roots of 2x² - 7x + 3 = 0, without solving for x.

For any equation ax² + bx + c = 0:

Sum of roots = -b/a
Product of roots = c/a

Here, a = 2, b = -7, c = 3.

Sum of roots = -(-7)/2 = 7/2 Product of roots = 3/2

Answer: Sum = 7/2, Product = 3/2

This shortcut is one of the fastest ways to pick up marks on JAMB — no need to fully solve the equation if the question only asks for sum or product.

Try It Yourself

Solve: x² - x - 6 = 0
Solve: x² + 7x + 10 = 0
Find the sum and product of the roots of 3x² + 5x - 2 = 0

Answers:

x = 3 or x = -2
x = -2 or x = -5
Sum = -5/3, Product = -2/3

Common Mistakes to Avoid

Forgetting that a quadratic equation has two roots, not one
Mixing up the signs when factorizing (double-check by expanding your factors back out)
Applying the sum/product shortcut with the wrong sign — remember it's -b/a, not b/a

Continue practicing with our JAMB Mathematics past questions or explore common mistakes students make in JAMB Mathematics. For the full subject breakdown, visit the JAMB Mathematics guide.