Discriminant
- CBSE · NCERT Class 10, Ch 4 Quadratic Equations
The discriminant of the quadratic equation ax² + bx + c = 0 is the number b² - 4ac, which tells you what kind of roots the equation has.
It is the part of the quadratic formula under the square root. You can find it without solving the equation. Its sign alone decides the nature of the roots:
- b² - 4ac > 0: two distinct real roots.
- b² - 4ac = 0: two equal real roots.
- b² - 4ac < 0: no real roots.
A small example
Take 3x² - 2x + 1 = 0. Here a = 3, b = -2 and c = 1. The discriminant is (-2)² - 4 × 3 × 1 = 4 - 12 = -8. It is negative, so there are no real roots. For x² - 6x + 9 = 0, it is 36 - 36 = 0. So the two roots are equal, and both are 3.
A question can ask for the value of k that gives equal roots. Then you set b² - 4ac = 0 and solve for k.
Where marks go
Question 24 of CBSE's 2025-26 Maths Basic sample paper asks for the nature of the roots of x² + 4x - 3√2 = 0, for 2 marks. The board's Maths Basic marking scheme for 2025-26 gives 1 mark for the discriminant, 16 + 12√2, being positive. It gives the other mark for the conclusion: the roots are real and distinct.
So the value is only half the marks. The answer needs the sentence that links the sign to the kind of roots. The signs inside matter too: -4 × 1 × (-3√2) is +12√2. Read more on how step marking works.
Sources
Facts last checked against these sources on 30 September 2026.
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