Free · Class 10 · 6 worksheets · answer keys · practise online · set 19
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 19
Name: Date: Score: / 10
Solve.
x² + 2x − 48 = 0 x² + 6x + 5 = 0 x² + 2x − 8 = 0 x² − 2x − 48 = 0 x² + 14x + 45 = 0 x² − 5x − 14 = 0 x² + 16x + 64 = 0 x² + 6x + 8 = 0 x² + 7x − 8 = 0 x² − 7x − 8 = 0
✅ Answer key — Solve by factorisation
x = −8 or x = 6 x = −5 or x = −1 x = −4 or x = 2 x = −6 or x = 8 x = −9 or x = −5 x = −2 or x = 7 x = −8 (equal roots) x = −4 or x = −2 x = −8 or x = 1 x = −1 or x = 8 TalentJR · talentjr.in/quadratic-equations-worksheet
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Factorisation (a ≠ 1) Class 10 · Worksheet 2 · set 19
Name: Date: Score: / 8
Solve by splitting the middle term.
2x² − 15x − 8 = 0 5x² + 2x − 3 = 0 3x² − 16x − 64 = 0 2x² − 7x − 9 = 0 2x² − 21x + 49 = 0 4x² + 9x + 5 = 0 5x² − 2x − 16 = 0 5x² − 32x − 64 = 0
✅ Answer key — Factorisation (a ≠ 1)
x = −1/2 or x = 8 x = −1 or x = 3/5 x = −8/3 or x = 8 x = −1 or x = 9/2 x = 7/2 or x = 7 x = −5/4 or x = −1 x = −8/5 or x = 2 x = −8/5 or x = 8 TalentJR · talentjr.in/quadratic-equations-worksheet
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Nature of roots Class 10 · Worksheet 3 · set 19
Name: Date: Score: / 8
Find the discriminant and the nature of the roots.
Nature of the roots of 4x² − 2x + 4 = 0 Nature of the roots of 4x² − 8x − 8 = 0 Nature of the roots of 2x² − 4x − 3 = 0 Nature of the roots of 4x² − 2x − 5 = 0 Nature of the roots of 5x² + 3x − 2 = 0 Nature of the roots of x² − 2 = 0 Nature of the roots of 4x² − 2x + 1 = 0 Nature of the roots of 5x² − 7x − 2 = 0
✅ Answer key — Nature of roots
D = −60 → no real roots D = 192 → two distinct real roots D = 40 → two distinct real roots D = 84 → two distinct real roots D = 49 → two distinct real roots D = 8 → two distinct real roots D = −12 → no real roots D = 89 → two distinct real roots TalentJR · talentjr.in/quadratic-equations-worksheet
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Quadratic formula Class 10 · Worksheet 4 · set 19
Name: Date: Score: / 6
Solve using the quadratic formula.
Solve by the quadratic formula: 3x² + 5x − 6 = 0 Solve by the quadratic formula: 3x² − x − 5 = 0 Solve by the quadratic formula: x² + 3x − 1 = 0 Solve by the quadratic formula: 3x² − 5x − 9 = 0 Solve by the quadratic formula: 4x² + x − 1 = 0 Solve by the quadratic formula: 2x² − 2x − 7 = 0
✅ Answer key — Quadratic formula
x = (−5 ± √97)/6 (≈ 0.81, −2.47) x = (1 ± √61)/6 (≈ 1.47, −1.14) x = (−3 ± √13)/2 (≈ 0.3, −3.3) x = (5 ± √133)/6 (≈ 2.76, −1.09) x = (−1 ± √17)/8 (≈ 0.39, −0.64) x = (1 ± √15)/2 (≈ 2.44, −1.44) TalentJR · talentjr.in/quadratic-equations-worksheet
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Find k Class 10 · Worksheet 5 · set 19
Name: Date: Score: / 6
Solve.
Find k if x² + 10x + k = 0 has equal roots. Find k if x² + kx + 64 = 0 has equal roots. Find k if x² + kx + 1 = 0 has equal roots. Find k if x² + 2x + k = 0 has equal roots. Find k if x² + 12x + k = 0 has equal roots. Find k if x² − 8x + k = 0 has equal roots.
✅ Answer key — Find k
k = 25 k = 16 or k = −16 k = 2 or k = −2 k = 1 k = 36 k = 16 TalentJR · talentjr.in/quadratic-equations-worksheet
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Word problems Class 10 · Worksheet 6 · set 19
Name: Date: Score: / 6
Form a quadratic equation and solve.
The product of two consecutive positive integers is 156. Find the integers. The length of a rectangular park is 7 m more than its width. Its area is 690 sq m. Find its length and width. The product of two consecutive positive integers is 56. Find the integers. The length of a rectangular park is 2 m more than its width. Its area is 224 sq m. Find its length and width. The sum of the squares of two consecutive positive integers is 613. Find the integers. The sum of the squares of two consecutive positive integers is 265. Find the integers.
✅ Answer key — Word problems
12 and 13 width 23 m, length 30 m 7 and 8 width 14 m, length 16 m 17 and 18 11 and 12 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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