Basics of Quadratic Equations and Their Roots

Quadratic equations appear in some SBI Clerk Prelims slots as a set of five questions, each giving two equations and asking you to compare the variables. Before the comparison trick works, you need the fundamentals rock solid, because a single sign error early on flips the whole answer. This topic builds that base so the later shortcuts sit on firm ground.

The Standard Form

Every quadratic can be written as ax² + bx + c = 0, where a, b and c are constants and a is never zero. In bank papers a is almost always 1, which is exactly why the fast factorization method works so smoothly. The two solutions of this equation are called its roots, and finding them quickly — not deriving them from first principles — is the entire skill the exam tests.

Standard form: ax² + bx + c = 0 (roots are the two values of x that satisfy it)

What the Roots Tell You

The sum of the roots equals −b/a and their product equals c/a. With a = 1 this simplifies beautifully: the two roots add up to −b and multiply to c. This single relationship is the engine behind the factorization shortcut, so commit it to memory now. It lets you read the roots almost directly off the coefficients without any long calculation once you have practised enough.

Why the Bank Format Is Different

Ordinary schools ask you to 'solve' a quadratic; SBI Clerk asks you to solve two of them and then decide whether x is greater than, less than, equal to, or not comparable with y. That means your goal is not a pretty derivation but the fastest correct pair of roots, followed by a clean comparison. Keeping that goal in view stops you from over-working each equation.

Solved Example

Example: x² − 7x + 12 = 0. Sum of roots = 7, product = 12. Two numbers that add to 7 and multiply to 12 are 3 and 4, so the roots are x = 3 and x = 4. Notice you never used the quadratic formula.

✗ Reaching for the quadratic formula on x² − 7x + 12  |  ✓ Reading roots 3 and 4 from sum 7, product 12

The Quadratic Formula as a Backup

You should know the formula x = [−b ± √(b² − 4ac)] / 2a even though you will rarely use it, because it is your safety net when a split refuses to appear. The part under the root, b² − 4ac, is the discriminant, and it decides the nature of the roots. In practice, if you find yourself reaching for this formula on a bank quadratic, it is a strong signal that you have misread a sign, since every SBI Clerk quadratic is constructed to factor into clean integers. Treat the formula as a diagnostic tool rather than your main method, and your speed will stay high.