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Class 10 Quadratic Equations: cheat sheet
CBSE Mathematics. Equations of the form ax² + bx + c = 0: solve by factorising or the quadratic formula, and use the discriminant to tell what kind of roots there are.
Key ideas
- A quadratic equation can be written as ax² + bx + c = 0 with a ≠ 0. It has at most two roots.
- Factorising: split bx into two terms whose coefficients multiply to ac and add to b, then factorise in pairs.
- If (x − p)(x − q) = 0, then x = p or x = q.
- The quadratic formula works for every quadratic equation.
- The discriminant D = b² − 4ac tells the nature of the roots without solving.
- In word problems, check every root makes sense: a length, speed or age cannot be negative.
Remember
| Quadratic formula | x = (−b ± √(b² − 4ac)) ÷ 2a |
| Discriminant | D = b² − 4ac |
| D > 0 | two distinct real roots |
| D = 0 | two equal real roots, each −b ÷ 2a |
| D < 0 | no real roots |
Watch out
- Dividing both sides by x and losing the root x = 0.
- Forgetting the ± and finding only one root.
- Using +b instead of −b in the formula when b is negative.
- Keeping a negative root for a length or an age.
Worked example
Solve: x + 18/x = 9 (x ≠ 0)
Working: multiply by x: x² − 9x + 18 = 0, so (x − 6)(x − 3) = 0
Answer: x = 3 or x = 6
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