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Quantitative Aptitude›Ch 4: Algebra, Geometry & Mensuration›Quadratic Equations
Master roots, relationships, and nature in seconds for SSC & Railway exams
Every quadratic equation of form ax² + bx + c = 0 has at most two roots. Use factorisation to split the middle term, and apply discriminant D = b² - 4ac to determine nature of roots instantly.
Quick Memory Hooks
| Discriminant (D) | Nature of Roots | Exam Implication |
|---|---|---|
| D > 0 | Real & Unequal | Two distinct solutions |
| D = 0 | Real & Equal | Both roots identical |
| D < 0 | Imaginary / No Real | Roots do not exist in R |
ax² + bx + c
(Standard Equation Form)
Standard Equation Form
Always arrange given terms in descending order of powers.
b² - 4ac
(Discriminant Value)
Discriminant Value
Calculate this first to check if roots can be found easily.
-b / a
(Sum of Roots Formula)
Sum of Roots Formula
Negative of x coefficient divided by x² coefficient.
c / a
(Product of Roots Formula)
Product of Roots Formula
Constant term divided by leading x² coefficient.
Forgetting negative sign in sum of roots (-b/a)Always use -b/a, never drop the negative sign
Missing the minus sign flips your entire answer and gives negative options in SSC.
Assuming quadratic form without checking a != 0Coefficient 'a' must never equal zero
If a = 0, the equation becomes linear, destroying the quadratic property completely.
Mixing up real equal roots condition (D > 0)Real and equal roots strictly require D = 0
Examiners bait you by interchanging D=0 and D>0 conditions in statement questions.
Q1.Find the sum of the roots of the quadratic equation 3x² - 12x + 7 = 0.
Q2.What is the nature of roots for the equation 2x² - 4x + 3 = 0?