What are the three methods to solve quadratic equations?

The three methods are: (1) Factorisation — split the middle term and factor; (2) Completing the square — convert to (x+p)² = q form; (3) Quadratic formula — x = (−b ± √(b²−4ac)) / 2a. For CBSE board exams, know all three methods as different questions specify which to use.

What does the discriminant tell us about roots?

The discriminant D = b² − 4ac tells us the nature of roots: D > 0 means two distinct real roots; D = 0 means two equal real roots (one repeated root); D < 0 means no real roots exist. Always calculate D first before solving.

How to solve quadratic equations by factorisation?

To factorise ax² + bx + c = 0: (1) Find two numbers p and q such that p × q = ac and p + q = b; (2) Rewrite bx as px + qx; (3) Group and factor; (4) Set each factor to zero and solve. Example: x² + 5x + 6 = 0 → (x+2)(x+3) = 0 → x = −2 or −3.

How to Solve Quadratic Equations

Q: How to solve quadratic equations by factorisation?

To factorise ax² + bx + c = 0: (1) Find two numbers p and q such that p × q = ac and p + q = b; (2) Rewrite bx as px + qx; (3) Group and factor; (4) Set each factor to zero and solve. Example: x² + 5x + 6 = 0 → (x+2)(x+3) = 0 → x = −2 or −3.

Quadratic Equations • Class 10 Mathematics • NCERT • CBSE

A quadratic equation has the form ax² + bx + c = 0 (a ≠ 0). Solve it using: (1) Factorisation, (2) Completing the square, or (3) Quadratic formula: x = (−b ± √(b²−4ac)) / 2a. The discriminant D = b²−4ac determines the nature of roots.

Key Formulas

ax² + bx + c = 0 (Standard form of quadratic equation)
x = (−b ± √(b²−4ac)) / 2a (Quadratic formula)
D = b² − 4ac (Discriminant)
Sum of roots α + β = −b/a
Product of roots αβ = c/a

Frequently Asked Questions

What are the three methods to solve quadratic equations?: The three methods are: (1) Factorisation — split the middle term and factor; (2) Completing the square — convert to (x+p)² = q form; (3) Quadratic formula — x = (−b ± √(b²−4ac)) / 2a. For CBSE board exams, know all three methods as different questions specify which to use.
What does the discriminant tell us about roots?: The discriminant D = b² − 4ac tells us the nature of roots: D > 0 means two distinct real roots; D = 0 means two equal real roots (one repeated root); D < 0 means no real roots exist. Always calculate D first before solving.
How to solve quadratic equations by factorisation?: To factorise ax² + bx + c = 0: (1) Find two numbers p and q such that p × q = ac and p + q = b; (2) Rewrite bx as px + qx; (3) Group and factor; (4) Set each factor to zero and solve. Example: x² + 5x + 6 = 0 → (x+2)(x+3) = 0 → x = −2 or −3.

Study With GyanAI

GyanAI's AI tutor can answer any question about this topic instantly. Try GyanAI free for step-by-step NCERT solutions aligned with the CBSE curriculum.