Quadratic Equations Tricks for Bank Exams

You don’t need both roots exactly — you need to know where x’s roots sit compared with y’s. Signs alone often decide it.

Finding roots fast

For x² + bx + c = 0, find two numbers whose product is c and whose sum is b; the roots are those numbers with signs flipped.
x² − 8x + 15 = 0 → (−3)(−5) = 15 and −3 + (−5) = −8 → (x − 3)(x − 5) = 0 → x = 3, 5.
For ax² + bx + c = 0, split the middle term using two numbers with product a × c and sum b: 2x² − 7x + 6 = 0 → −3 and −4 (product 12, sum −7) → 2x² − 4x − 3x + 6 = (2x − 3)(x − 2) → x = 1.5, 2.
x² = k gives x = +√k and −√k: x² − 4 = 0 → x = 2, −2.

b positive, c positive → both roots negative (x² + 5x + 6 → −2, −3).
b negative, c positive → both roots positive (x² − 5x + 6 → 2, 3).
b positive, c negative → one positive, one negative; the larger one in size is negative (x² + x − 6 → 2, −3).
b negative, c negative → one positive, one negative; the larger one in size is positive (x² − x − 6 → 3, −2).

Compare every root of x with every root of y.
Every x bigger than every y → x > y. Every x bigger or equal (at least one tie) → x ≥ y.
Mirror rules give x < y and x ≤ y. A single shared value with no other roots → x = y.
If some pairs go one way and some the other → relationship cannot be determined.
Example: x = 3, 5 and y = −7, −10 → every x is bigger → x > y.

Looking for the exam itself? See the exam patterns for SBI, IBPS and RRB.