Solution by factorisation
- CBSE · NCERT Class 10, Ch 4 Quadratic Equations
Solving a quadratic equation by factorisation means writing it as two linear factors multiplied to give 0, then setting each factor equal to 0.
If two numbers multiply to give 0, at least one of them must be 0. So once ax² + bx + c = 0 is written as two brackets multiplied together, each bracket gives a root. To factorise, split the middle term bx into two parts. Their coefficients must add to b and multiply to a × c.
A small example
Solve n² + 3n - 180 = 0. You need two numbers that add to 3 and multiply to -180. They are 15 and -12.
- n² + 15n - 12n - 180 = 0
- n(n + 15) - 12(n + 15) = 0
- (n + 15)(n - 12) = 0
- So n = -15 or n = 12.
Where marks go
This equation comes from Question 28(A) of CBSE's 2026-27 Maths Standard sample paper. A polygon's exterior angles form an arithmetic progression that starts at 8° and rises by 4° each time. They add up to 360°, which gives the equation above.
The board's Maths Standard marking scheme for 2026-27 gives 1 mark for forming the equation and 1 mark for the factorisation. Half a mark is for the two roots, -15 and 12. The last half mark is for rejecting -15 and keeping n = 12. A polygon cannot have a negative number of sides. Each of these is a separate step under step marking.
Sources
Facts last checked against these sources on 30 September 2026.
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