Free · Class 10 · 6 worksheets · answer keys · practise online · set 77
Quadratic equations worksheets — Class 10, with answers
Free Class 10 quadratic equations worksheets: solve by factorisation, quadratic formula, nature of roots (discriminant), find k for equal roots and word problems — with answers.
💡 Learn it first
A quadratic equation is ax² + bx + c = 0 (a ≠ 0). It has at most two roots. Factorisation : split the middle term — x² − 5x + 6 = (x − 2)(x − 3) = 0 → x = 2 or 3.Quadratic formula : x = (−b ± √D) / 2a, where D = b² − 4ac . D > 0: two distinct real roots; D = 0: equal roots; D < 0: no real roots.
Solve by factorisation (Class 10) Factorisation (a ≠ 1) (Class 10) Nature of roots (Class 10) Quadratic formula (Class 10) Find k (Class 10) Word problems (Class 10)
Solve by factorisation Class 10 · Worksheet 1 · set 77
Name: Date: Score: / 10
Solve.
x² + 3x − 4 = 0 x² − 8x + 15 = 0 x² − 4x + 4 = 0 x² + 10x + 9 = 0 x² + x − 56 = 0 x² − 11x + 24 = 0 x² + 5x + 6 = 0 x² − 7x − 8 = 0 x² − x − 30 = 0 x² − 5x − 36 = 0
✅ Answer key — Solve by factorisation
x = −4 or x = 1 x = 3 or x = 5 x = 2 (equal roots) x = −9 or x = −1 x = −8 or x = 7 x = 3 or x = 8 x = −3 or x = −2 x = −1 or x = 8 x = −5 or x = 6 x = −4 or x = 9 TalentJR · talentjr.in/quadratic-equations-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Factorisation (a ≠ 1) Class 10 · Worksheet 2 · set 77
Name: Date: Score: / 8
Solve by splitting the middle term.
3x² + 26x + 16 = 0 5x² − 23x + 12 = 0 3x² + 16x − 35 = 0 3x² − 17x − 56 = 0 4x² + x − 18 = 0 3x² + 17x + 24 = 0 3x² + 29x + 56 = 0 4x² + 29x + 45 = 0
✅ Answer key — Factorisation (a ≠ 1)
x = −8 or x = −2/3 x = 3/5 or x = 4 x = −7 or x = 5/3 x = −7/3 or x = 8 x = −9/4 or x = 2 x = −3 or x = −8/3 x = −7 or x = −8/3 x = −5 or x = −9/4 TalentJR · talentjr.in/quadratic-equations-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Nature of roots Class 10 · Worksheet 3 · set 77
Name: Date: Score: / 8
Find the discriminant and the nature of the roots.
Nature of the roots of 4x² − 4x − 4 = 0 Nature of the roots of 2x² + 7x + 3 = 0 Nature of the roots of 2x² + 5x + 1 = 0 Nature of the roots of 3x² + 9x − 4 = 0 Nature of the roots of 5x² − 6x + 7 = 0 Nature of the roots of 2x² − 3x + 1 = 0 Nature of the roots of x² − 8x + 1 = 0 Nature of the roots of x² − 9x − 4 = 0
✅ Answer key — Nature of roots
D = 80 → two distinct real roots D = 25 → two distinct real roots D = 17 → two distinct real roots D = 129 → two distinct real roots D = −104 → no real roots D = 1 → two distinct real roots D = 60 → two distinct real roots D = 97 → two distinct real roots TalentJR · talentjr.in/quadratic-equations-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Quadratic formula Class 10 · Worksheet 4 · set 77
Name: Date: Score: / 6
Solve using the quadratic formula.
Solve by the quadratic formula: x² − 2 = 0 Solve by the quadratic formula: 2x² − 2x − 2 = 0 Solve by the quadratic formula: x² − 7x + 9 = 0 Solve by the quadratic formula: x² − 8x − 3 = 0 Solve by the quadratic formula: 2x² − 2x − 1 = 0 Solve by the quadratic formula: x² + 6x + 6 = 0
✅ Answer key — Quadratic formula
x = ±√2 (≈ 1.41, −1.41) x = (1 ± √5)/2 (≈ 1.62, −0.62) x = (7 ± √13)/2 (≈ 5.3, 1.7) x = 4 ± √19 (≈ 8.36, −0.36) x = (1 ± √3)/2 (≈ 1.37, −0.37) x = −3 ± √3 (≈ −1.27, −4.73) TalentJR · talentjr.in/quadratic-equations-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Find k Class 10 · Worksheet 5 · set 77
Name: Date: Score: / 6
Solve.
Find k if x² + 10x + k = 0 has equal roots. Find k if x² + kx + 16 = 0 has equal roots. Find k if x² + kx + 4 = 0 has equal roots. Find k if x² + kx + 36 = 0 has equal roots. Find k if x² + kx + 81 = 0 has equal roots. Find k if x² + 16x + k = 0 has equal roots.
✅ Answer key — Find k
k = 25 k = 8 or k = −8 k = 4 or k = −4 k = 12 or k = −12 k = 18 or k = −18 k = 64 TalentJR · talentjr.in/quadratic-equations-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Word problems Class 10 · Worksheet 6 · set 77
Name: Date: Score: / 6
Form a quadratic equation and solve.
The product of two consecutive positive integers is 702. Find the integers. The length of a rectangular park is 9 m more than its width. Its area is 36 sq m. Find its length and width. The length of a rectangular park is 5 m more than its width. Its area is 36 sq m. Find its length and width. The length of a rectangular park is 3 m more than its width. Its area is 70 sq m. Find its length and width. The length of a rectangular park is 9 m more than its width. Its area is 532 sq m. Find its length and width. The sum of the squares of two consecutive positive integers is 761. Find the integers.
✅ Answer key — Word problems
26 and 27 width 3 m, length 12 m width 4 m, length 9 m width 7 m, length 10 m width 19 m, length 28 m 19 and 20 TalentJR · talentjr.in/quadratic-equations-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Questions
What is the discriminant? D = b² − 4ac. It tells the nature of the roots without solving: positive → two real roots, zero → equal roots, negative → no real roots.
Are these worksheets free? Yes — print them or save as PDF free. Every worksheet has an answer key.
How do I get different questions? Press “🔄 New set” — the questions change (maths numbers are new every time; English sentences are shuffled).
How do I print only one worksheet? Press “🖨️ Print” on that worksheet. Tick “with answer key” if you want the answers on a second page.
Can my child do this worksheet online, like a quiz? Yes — press “▶️ Practise online” on any worksheet. The questions come one at a time with instant marking, a score at the end and a review of mistakes. No sign-in is needed.
