Free · Class 10 · 6 worksheets · answer keys · practise online · set 26
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 26
Name: Date: Score: / 10
Solve.
x² + 2x − 24 = 0 x² + 11x + 28 = 0 x² − 3x − 4 = 0 x² − 25 = 0 x² − 13x + 42 = 0 x² + 5x − 24 = 0 x² − 8x + 16 = 0 x² + 9x + 14 = 0 x² + 9x + 8 = 0 x² − 10x + 24 = 0
✅ Answer key — Solve by factorisation
x = −6 or x = 4 x = −7 or x = −4 x = −1 or x = 4 x = −5 or x = 5 x = 6 or x = 7 x = −8 or x = 3 x = 4 (equal roots) x = −7 or x = −2 x = −8 or x = −1 x = 4 or x = 6 TalentJR · talentjr.in/quadratic-equations-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Factorisation (a ≠ 1) Class 10 · Worksheet 2 · set 26
Name: Date: Score: / 8
Solve by splitting the middle term.
5x² − 22x − 48 = 0 5x² + 44x − 9 = 0 5x² − 6x + 1 = 0 3x² + 29x + 40 = 0 5x² + 37x + 42 = 0 5x² + 21x + 18 = 0 5x² − 37x − 24 = 0 4x² − 31x − 8 = 0
✅ Answer key — Factorisation (a ≠ 1)
x = −8/5 or x = 6 x = −9 or x = 1/5 x = 1/5 or x = 1 x = −8 or x = −5/3 x = −6 or x = −7/5 x = −3 or x = −6/5 x = −3/5 or x = 8 x = −1/4 or x = 8 TalentJR · talentjr.in/quadratic-equations-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Nature of roots Class 10 · Worksheet 3 · set 26
Name: Date: Score: / 8
Find the discriminant and the nature of the roots.
Nature of the roots of 4x² + 5x + 6 = 0 Nature of the roots of 2x² + 6x + 3 = 0 Nature of the roots of 5x² + 4x + 5 = 0 Nature of the roots of 2x² − 5x − 7 = 0 Nature of the roots of x² − 6x − 9 = 0 Nature of the roots of 2x² + 2x + 4 = 0 Nature of the roots of x² + 9x − 6 = 0 Nature of the roots of 5x² − 4x + 9 = 0
✅ Answer key — Nature of roots
D = −71 → no real roots D = 12 → two distinct real roots D = −84 → no real roots D = 81 → two distinct real roots D = 72 → two distinct real roots D = −28 → no real roots D = 105 → two distinct real roots D = −164 → no real roots TalentJR · talentjr.in/quadratic-equations-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Quadratic formula Class 10 · Worksheet 4 · set 26
Name: Date: Score: / 6
Solve using the quadratic formula.
Solve by the quadratic formula: 2x² − 4x − 4 = 0 Solve by the quadratic formula: x² − 2x − 9 = 0 Solve by the quadratic formula: x² − 9x + 5 = 0 Solve by the quadratic formula: x² + 8x − 4 = 0 Solve by the quadratic formula: x² − 6 = 0 Solve by the quadratic formula: 2x² + 5x + 1 = 0
✅ Answer key — Quadratic formula
x = 1 ± √3 (≈ 2.73, −0.73) x = 1 ± √10 (≈ 4.16, −2.16) x = (9 ± √61)/2 (≈ 8.41, 0.59) x = −4 ± 2√5 (≈ 0.47, −8.47) x = ±√6 (≈ 2.45, −2.45) x = (−5 ± √17)/4 (≈ −0.22, −2.28) TalentJR · talentjr.in/quadratic-equations-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Find k Class 10 · Worksheet 5 · set 26
Name: Date: Score: / 6
Solve.
Find k if x² − 18x + k = 0 has equal roots. Find k if x² + kx + 1 = 0 has equal roots. Find k if x² + kx + 49 = 0 has equal roots. Find k if x² − 2x + k = 0 has equal roots. Find k if x² + 16x + k = 0 has equal roots. Find k if x² + 6x + k = 0 has equal roots.
✅ Answer key — Find k
k = 81 k = 2 or k = −2 k = 14 or k = −14 k = 1 k = 64 k = 9 TalentJR · talentjr.in/quadratic-equations-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Word problems Class 10 · Worksheet 6 · set 26
Name: Date: Score: / 6
Form a quadratic equation and solve.
The product of two consecutive positive integers is 342. Find the integers. 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 product of two consecutive positive integers is 110. Find the integers. The length of a rectangular park is 6 m more than its width. Its area is 40 sq m. Find its length and width. The length of a rectangular park is 2 m more than its width. Its area is 195 sq m. Find its length and width. The product of two consecutive positive integers is 240. Find the integers.
✅ Answer key — Word problems
18 and 19 width 19 m, length 28 m 10 and 11 width 4 m, length 10 m width 13 m, length 15 m 15 and 16 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.
