Free · Class 10 · 6 worksheets · answer keys · practise online · set 42
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 42
Name: Date: Score: / 10
Solve.
x² + x − 12 = 0 x² − 8x + 16 = 0 x² + 7x + 12 = 0 x² − 4x − 45 = 0 x² + 3x − 18 = 0 x² + 2x − 3 = 0 x² + 9x + 8 = 0 x² − 4x − 21 = 0 x² + 18x + 81 = 0 x² − 16x + 64 = 0
✅ Answer key — Solve by factorisation
x = −4 or x = 3 x = 4 (equal roots) x = −4 or x = −3 x = −5 or x = 9 x = −6 or x = 3 x = −3 or x = 1 x = −8 or x = −1 x = −3 or x = 7 x = −9 (equal roots) x = 8 (equal roots) TalentJR · talentjr.in/quadratic-equations-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Factorisation (a ≠ 1) Class 10 · Worksheet 2 · set 42
Name: Date: Score: / 8
Solve by splitting the middle term.
2x² + 7x − 72 = 0 3x² + 11x + 8 = 0 3x² − 8x − 3 = 0 2x² + 5x − 3 = 0 5x² + 33x + 18 = 0 2x² + 17x + 8 = 0 3x² − 4x − 7 = 0 5x² + 23x + 12 = 0
✅ Answer key — Factorisation (a ≠ 1)
x = −8 or x = 9/2 x = −8/3 or x = −1 x = −1/3 or x = 3 x = −3 or x = 1/2 x = −6 or x = −3/5 x = −8 or x = −1/2 x = −1 or x = 7/3 x = −4 or x = −3/5 TalentJR · talentjr.in/quadratic-equations-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Nature of roots Class 10 · Worksheet 3 · set 42
Name: Date: Score: / 8
Find the discriminant and the nature of the roots.
Nature of the roots of 5x² + 1 = 0 Nature of the roots of x² + 4x − 4 = 0 Nature of the roots of 3x² − 6x − 6 = 0 Nature of the roots of 5x² − 8x + 2 = 0 Nature of the roots of 4x² + 9 = 0 Nature of the roots of x² + 9x + 1 = 0 Nature of the roots of 3x² − 6x + 8 = 0 Nature of the roots of 5x² + 2 = 0
✅ Answer key — Nature of roots
D = −20 → no real roots D = 32 → two distinct real roots D = 108 → two distinct real roots D = 24 → two distinct real roots D = −144 → no real roots D = 77 → two distinct real roots D = −60 → no real roots D = −40 → no real roots TalentJR · talentjr.in/quadratic-equations-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Quadratic formula Class 10 · Worksheet 4 · set 42
Name: Date: Score: / 6
Solve using the quadratic formula.
Solve by the quadratic formula: 3x² − 2x − 6 = 0 Solve by the quadratic formula: 4x² − 4x − 9 = 0 Solve by the quadratic formula: x² + 2x − 4 = 0 Solve by the quadratic formula: 4x² + 6x − 8 = 0 Solve by the quadratic formula: 2x² + 5x + 1 = 0 Solve by the quadratic formula: 2x² − 4x − 7 = 0
✅ Answer key — Quadratic formula
x = (1 ± √19)/3 (≈ 1.79, −1.12) x = (1 ± √10)/2 (≈ 2.08, −1.08) x = −1 ± √5 (≈ 1.24, −3.24) x = (−3 ± √41)/4 (≈ 0.85, −2.35) x = (−5 ± √17)/4 (≈ −0.22, −2.28) x = (2 ± 3√2)/2 (≈ 3.12, −1.12) TalentJR · talentjr.in/quadratic-equations-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Find k Class 10 · Worksheet 5 · set 42
Name: Date: Score: / 6
Solve.
Find k if x² + 4x + k = 0 has equal roots. Find k if x² + 6x + k = 0 has equal roots. Find k if x² − 8x + k = 0 has equal roots. Find k if x² − 12x + k = 0 has equal roots. Find k if x² + kx + 49 = 0 has equal roots. Find k if x² − 18x + k = 0 has equal roots.
✅ Answer key — Find k
k = 4 k = 9 k = 16 k = 36 k = 14 or k = −14 k = 81 TalentJR · talentjr.in/quadratic-equations-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Word problems Class 10 · Worksheet 6 · set 42
Name: Date: Score: / 6
Form a quadratic equation and solve.
The product of two consecutive positive integers is 870. Find the integers. The sum of the squares of two consecutive positive integers is 421. Find the integers. The sum of the squares of two consecutive positive integers is 365. Find the integers. The sum of the squares of two consecutive positive integers is 145. Find the integers. The sum of the squares of two consecutive positive integers is 313. Find the integers. The sum of the squares of two consecutive positive integers is 181. Find the integers.
✅ Answer key — Word problems
29 and 30 14 and 15 13 and 14 8 and 9 12 and 13 9 and 10 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.
