Free · Class 10 · 6 worksheets · answer keys · practise online · set 41
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 41
Name: Date: Score: / 10
Solve.
x² − 5x + 4 = 0 x² − x − 72 = 0 x² − 7x − 18 = 0 x² − 12x + 35 = 0 x² + 2x − 35 = 0 x² − 15x + 56 = 0 x² + 5x − 36 = 0 x² − 8x + 16 = 0 x² − 10x + 16 = 0 x² − 1 = 0
✅ Answer key — Solve by factorisation
x = 1 or x = 4 x = −8 or x = 9 x = −2 or x = 9 x = 5 or x = 7 x = −7 or x = 5 x = 7 or x = 8 x = −9 or x = 4 x = 4 (equal roots) x = 2 or x = 8 x = −1 or x = 1 TalentJR · talentjr.in/quadratic-equations-worksheet
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Factorisation (a ≠ 1) Class 10 · Worksheet 2 · set 41
Name: Date: Score: / 8
Solve by splitting the middle term.
2x² − 13x − 7 = 0 2x² + 7x − 30 = 0 4x² − 23x + 15 = 0 4x² − 19x − 63 = 0 4x² − 3x − 7 = 0 4x² + 31x − 8 = 0 2x² + 11x + 12 = 0 2x² + 19x + 45 = 0
✅ Answer key — Factorisation (a ≠ 1)
x = −1/2 or x = 7 x = −6 or x = 5/2 x = 3/4 or x = 5 x = −9/4 or x = 7 x = −1 or x = 7/4 x = −8 or x = 1/4 x = −4 or x = −3/2 x = −5 or x = −9/2 TalentJR · talentjr.in/quadratic-equations-worksheet
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Nature of roots Class 10 · Worksheet 3 · set 41
Name: Date: Score: / 8
Find the discriminant and the nature of the roots.
Nature of the roots of 2x² + 7x − 3 = 0 Nature of the roots of 3x² + 3x − 5 = 0 Nature of the roots of 5x² + 2x + 1 = 0 Nature of the roots of 4x² + 4x + 4 = 0 Nature of the roots of 4x² − 4x − 6 = 0 Nature of the roots of 3x² + 4x − 4 = 0 Nature of the roots of 2x² + 9 = 0 Nature of the roots of 2x² + 9x + 8 = 0
✅ Answer key — Nature of roots
D = 73 → two distinct real roots D = 69 → two distinct real roots D = −16 → no real roots D = −48 → no real roots D = 112 → two distinct real roots D = 64 → two distinct real roots D = −72 → no real roots D = 17 → two distinct real roots TalentJR · talentjr.in/quadratic-equations-worksheet
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Quadratic formula Class 10 · Worksheet 4 · set 41
Name: Date: Score: / 6
Solve using the quadratic formula.
Solve by the quadratic formula: x² − 9x − 3 = 0 Solve by the quadratic formula: 2x² − 2x − 2 = 0 Solve by the quadratic formula: 3x² − 6x + 1 = 0 Solve by the quadratic formula: 2x² + 6x − 5 = 0 Solve by the quadratic formula: x² + 3x − 9 = 0 Solve by the quadratic formula: 4x² − 3x − 5 = 0
✅ Answer key — Quadratic formula
x = (9 ± √93)/2 (≈ 9.32, −0.32) x = (1 ± √5)/2 (≈ 1.62, −0.62) x = (3 ± √6)/3 (≈ 1.82, 0.18) x = (−3 ± √19)/2 (≈ 0.68, −3.68) x = (−3 ± 3√5)/2 (≈ 1.85, −4.85) x = (3 ± √89)/8 (≈ 1.55, −0.8) TalentJR · talentjr.in/quadratic-equations-worksheet
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Find k Class 10 · Worksheet 5 · set 41
Name: Date: Score: / 6
Solve.
Find k if x² + kx + 49 = 0 has equal roots. Find k if x² − 6x + k = 0 has equal roots. Find k if x² + kx + 81 = 0 has equal roots. Find k if x² + kx + 1 = 0 has equal roots. Find k if x² − 12x + k = 0 has equal roots. Find k if x² − 18x + k = 0 has equal roots.
✅ Answer key — Find k
k = 14 or k = −14 k = 9 k = 18 or k = −18 k = 2 or k = −2 k = 36 k = 81 TalentJR · talentjr.in/quadratic-equations-worksheet
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Word problems Class 10 · Worksheet 6 · set 41
Name: Date: Score: / 6
Form a quadratic equation and solve.
The length of a rectangular park is 10 m more than its width. Its area is 704 sq m. Find its length and width. The product of two consecutive positive integers is 306. 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 3 m more than its width. Its area is 54 sq m. Find its length and width. The product of two consecutive positive integers is 380. Find the integers. The product of two consecutive positive integers is 600. Find the integers.
✅ Answer key — Word problems
width 22 m, length 32 m 17 and 18 width 3 m, length 12 m width 6 m, length 9 m 19 and 20 24 and 25 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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