Free · Class 10 · 6 worksheets · answer keys · practise online · set 68
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.
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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 68
Name: Date: Score: / 10
Solve.
x² − 7x + 10 = 0 x² + 14x + 45 = 0 x² − 6x − 16 = 0 x² + 8x + 16 = 0 x² + 7x + 10 = 0 x² + 9x + 18 = 0 x² + 9x + 20 = 0 x² − 4x − 32 = 0 x² + 2x − 48 = 0 x² − x − 30 = 0
✅ Answer key — Solve by factorisation
x = 2 or x = 5 x = −9 or x = −5 x = −2 or x = 8 x = −4 (equal roots) x = −5 or x = −2 x = −6 or x = −3 x = −5 or x = −4 x = −4 or x = 8 x = −8 or x = 6 x = −5 or x = 6 TalentJR · talentjr.in/quadratic-equations-worksheet
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Factorisation (a ≠ 1) Class 10 · Worksheet 2 · set 68
Name: Date: Score: / 8
Solve by splitting the middle term.
3x² + 7x + 4 = 0 3x² − 20x − 7 = 0 5x² + 4x − 1 = 0 3x² + 2x − 21 = 0 5x² − 16x − 45 = 0 4x² − 23x − 35 = 0 2x² − 15x + 28 = 0 2x² + 9x − 56 = 0
✅ Answer key — Factorisation (a ≠ 1)
x = −4/3 or x = −1 x = −1/3 or x = 7 x = −1 or x = 1/5 x = −3 or x = 7/3 x = −9/5 or x = 5 x = −5/4 or x = 7 x = 7/2 or x = 4 x = −8 or x = 7/2 TalentJR · talentjr.in/quadratic-equations-worksheet
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Nature of roots Class 10 · Worksheet 3 · set 68
Name: Date: Score: / 8
Find the discriminant and the nature of the roots.
Nature of the roots of 2x² − 5x + 1 = 0 Nature of the roots of 2x² − 3x + 4 = 0 Nature of the roots of 5x² + 9x − 4 = 0 Nature of the roots of 2x² − 2x − 4 = 0 Nature of the roots of 4x² − 5x + 4 = 0 Nature of the roots of x² + 8x − 3 = 0 Nature of the roots of 5x² + 5x + 1 = 0 Nature of the roots of 5x² − x − 9 = 0
✅ Answer key — Nature of roots
D = 17 → two distinct real roots D = −23 → no real roots D = 161 → two distinct real roots D = 36 → two distinct real roots D = −39 → no real roots D = 76 → two distinct real roots D = 5 → two distinct real roots D = 181 → two distinct real roots TalentJR · talentjr.in/quadratic-equations-worksheet
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Quadratic formula Class 10 · Worksheet 4 · set 68
Name: Date: Score: / 6
Solve using the quadratic formula.
Solve by the quadratic formula: 2x² − 7x + 4 = 0 Solve by the quadratic formula: x² − 3x − 3 = 0 Solve by the quadratic formula: 4x² − 8 = 0 Solve by the quadratic formula: 3x² + 2x − 6 = 0 Solve by the quadratic formula: 3x² + 4x − 3 = 0 Solve by the quadratic formula: 3x² + 5x + 1 = 0
✅ Answer key — Quadratic formula
x = (7 ± √17)/4 (≈ 2.78, 0.72) x = (3 ± √21)/2 (≈ 3.79, −0.79) x = ±√2 (≈ 1.41, −1.41) x = (−1 ± √19)/3 (≈ 1.12, −1.79) x = (−2 ± √13)/3 (≈ 0.54, −1.87) x = (−5 ± √13)/6 (≈ −0.23, −1.43) TalentJR · talentjr.in/quadratic-equations-worksheet
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Find k Class 10 · Worksheet 5 · set 68
Name: Date: Score: / 6
Solve.
Find k if x² + kx + 36 = 0 has equal roots. Find k if x² − 18x + 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 + 9 = 0 has equal roots. Find k if x² + kx + 4 = 0 has equal roots.
✅ Answer key — Find k
k = 12 or k = −12 k = 81 k = 16 k = 36 k = 6 or k = −6 k = 4 or k = −4 TalentJR · talentjr.in/quadratic-equations-worksheet
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Word problems Class 10 · Worksheet 6 · set 68
Name: Date: Score: / 6
Form a quadratic equation and solve.
The sum of the squares of two consecutive positive integers is 61. Find the integers. The length of a rectangular park is 9 m more than its width. Its area is 90 sq m. Find its length and width. The length of a rectangular park is 7 m more than its width. Its area is 588 sq m. Find its length and width. The length of a rectangular park is 10 m more than its width. Its area is 200 sq m. Find its length and width. The length of a rectangular park is 4 m more than its width. Its area is 192 sq m. Find its length and width. The length of a rectangular park is 9 m more than its width. Its area is 360 sq m. Find its length and width.
✅ Answer key — Word problems
5 and 6 width 6 m, length 15 m width 21 m, length 28 m width 10 m, length 20 m width 12 m, length 16 m width 15 m, length 24 m TalentJR · talentjr.in/quadratic-equations-worksheet
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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.
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