Solving quadratic equations: Class 10 practice
A quadratic ax² + bx + c = 0 has roots x = [−b ± √(b² − 4ac)] / 2a. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Factorising
- Square roots
The idea behind solving quadratic equations
A quadratic ax² + bx + c = 0 has roots x = [−b ± √(b² − 4ac)] / 2a. The discriminant D = b² − 4ac tells you the nature of the roots: D > 0 two real roots, D = 0 equal roots, D < 0 no real roots.
Step-by-step method
- Write in standard form.
- Compute D = b² − 4ac.
- Factorise by splitting the middle term, or use the formula.
- Check by substitution.
Worked example 1 (Basic)
Solve x² − 12x + 35 = 0.
- D = (-12)² − 4(1)(35) = 4
- Factorise: (x − 5)(x − 7) = 0
- x = 5 or x = 7
- Answer: x = 5, 7
Worked example 2 (Standard)
Solve x² − 8x + 7 = 0.
- D = (-8)² − 4(1)(7) = 36
- Factorise: (x − 1)(x − 7) = 0
- x = 1 or x = 7
- Answer: x = 1, 7
Worked example 3 (Challenge)
Solve 3x² + 20x + 12 = 0.
- D = (20)² − 4(3)(12) = 256
- Factorise: (3x + 2)(x + 6) = 0
- x = -2/3 or x = -6
- Answer: x = -2/3, -6
Common mistakes and misconceptions
- Sign error in −b
- Dividing only √D by 2a
Practice questions
- (Basic) Solve x² − 5x − 6 = 0.
- (Basic) Solve x² − 5x + 4 = 0.
- (Standard) Solve x² − 8x + 15 = 0.
- (Standard) Solve x² + 2x − 15 = 0.
- (Challenge) Solve 2x² − 11x + 5 = 0.
- (Challenge) Solve 2x² − 9x − 35 = 0.
Answer key with full working
- Q1: D = (-5)² − 4(1)(-6) = 49 → Factorise: (x + 1)(x − 6) = 0 → x = -1 or x = 6 → Answer: x = -1, 6
- Q2: D = (-5)² − 4(1)(4) = 9 → Factorise: (x − 1)(x − 4) = 0 → x = 1 or x = 4 → Answer: x = 1, 4
- Q3: D = (-8)² − 4(1)(15) = 4 → Factorise: (x − 5)(x − 3) = 0 → x = 5 or x = 3 → Answer: x = 5, 3
- Q4: D = (2)² − 4(1)(-15) = 64 → Factorise: (x − 3)(x + 5) = 0 → x = 3 or x = -5 → Answer: x = 3, -5
- Q5: D = (-11)² − 4(2)(5) = 81 → Factorise: (2x − 1)(x − 5) = 0 → x = 1/2 or x = 5 → Answer: x = 1/2, 5
- Q6: D = (-9)² − 4(2)(-35) = 361 → Factorise: (2x + 5)(x − 7) = 0 → x = -5/2 or x = 7 → Answer: x = -5/2, 7
Syllabus note
This skill is listed under "Quadratic Equations" for Class 10 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is solving quadratic equations in?
"Quadratic Equations", Class 10 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.