Quadratic formula
- CBSE · NCERT Class 10, Ch 4 Quadratic Equations
The quadratic formula gives the roots of ax² + bx + c = 0 as x = (-b ± √(b² - 4ac))/2a, if b² - 4ac is not negative.
It works for every quadratic equation, even when factorising is hard. The ± sign gives two roots: one with plus, one with minus. The part under the root, b² - 4ac, is the discriminant. If it is negative, there are no real roots. The chapter credits the Indian mathematician Sridharacharya with an early form of this formula.
A small example
A train covers 360 km at a steady speed. If it were 5 km/h faster, it would take 1 hour less. Let the speed be x km/h. Then 360/x - 360/(x + 5) = 1, which simplifies to x² + 5x - 1800 = 0.
- a = 1, b = 5 and c = -1800.
- b² - 4ac = 25 + 7200 = 7225, and √7225 = 85.
- x = (-5 ± 85)/2, so x = 40 or x = -45.
- A speed cannot be negative, so the speed is 40 km/h.
Where marks go
This is Question 33(A) of CBSE's 2026-27 Maths Basic sample paper, worth 5 marks. The board's Maths Basic marking scheme for 2026-27 gives half a mark for naming the two speeds and 1 mark for the time equation. It gives 1 mark for x² + 5x - 1800 = 0 and 1 mark for the formula with the numbers put in. The roots 40 and -45 earn 1 mark, and choosing 40 earns the last half.
So writing the formula with the right values is a mark on its own, before any arithmetic. That is step marking at work.
Sources
Facts last checked against these sources on 30 September 2026.
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