Quadratic equation
- CBSE · NCERT Class 10, Ch 4 Quadratic Equations
A quadratic equation is an equation that can be written as ax² + bx + c = 0, where a is not 0.
It is a quadratic polynomial set equal to zero. Unlike a linear equation, it has an x² term. The values of x that make it true are its roots. A quadratic equation has at most two roots. Word problems about area, speed or age can lead to one.
A small example
A park is 50 m by 40 m. A swimming pool sits in the middle, with a grass strip of the same width x all round. The grass covers 1184 m². So the pool is (50 - 2x) m by (40 - 2x) m.
- Grass = park - pool: 2000 - (50 - 2x)(40 - 2x) = 1184.
- This simplifies to x² - 45x + 296 = 0.
- Factorise: (x - 8)(x - 37) = 0, so x = 8 or x = 37.
- x = 37 is rejected, since the pool's sides would be negative. So x = 8, and the pool is 34 m by 24 m.
Where marks go
This is Question 32 of CBSE's 2026-27 Maths Standard sample paper, worth 5 marks. The board's Maths Standard marking scheme for 2026-27 gives half a mark for the pool's sides in terms of x. It gives 1 mark for the area equation and 1 for x² - 45x + 296 = 0. The factorisation earns half a mark.
A full mark goes to rejecting x = 37 and keeping x = 8. The last two half marks are the pool's length and breadth. So two roots, left unchecked against the question, stop short of the scheme's steps. Each line is its own step under step marking. The factorisation method page shows the splitting step in detail.
Sources
Facts last checked against these sources on 30 September 2026.
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