Free · Class 10 · 6 worksheets · answer keys · practise online · set 22
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 22
Name: Date: Score: / 10
Solve.
x² + x − 72 = 0 x² − x − 56 = 0 x² + 4x − 45 = 0 x² + 12x + 32 = 0 x² − 9x + 18 = 0 x² − 9x + 8 = 0 x² + x − 30 = 0 x² − 6x + 8 = 0 x² + 14x + 49 = 0 x² + x − 56 = 0
✅ Answer key — Solve by factorisation
x = −9 or x = 8 x = −7 or x = 8 x = −9 or x = 5 x = −8 or x = −4 x = 3 or x = 6 x = 1 or x = 8 x = −6 or x = 5 x = 2 or x = 4 x = −7 (equal roots) x = −8 or x = 7 TalentJR · talentjr.in/quadratic-equations-worksheet
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Factorisation (a ≠ 1) Class 10 · Worksheet 2 · set 22
Name: Date: Score: / 8
Solve by splitting the middle term.
2x² − 3x + 1 = 0 5x² − x − 6 = 0 4x² − 39x + 27 = 0 5x² − 17x − 40 = 0 4x² − 9x + 2 = 0 3x² + x − 4 = 0 5x² + 34x + 24 = 0 3x² − 29x + 56 = 0
✅ Answer key — Factorisation (a ≠ 1)
x = 1/2 or x = 1 x = −1 or x = 6/5 x = 3/4 or x = 9 x = −8/5 or x = 5 x = 1/4 or x = 2 x = −4/3 or x = 1 x = −6 or x = −4/5 x = 8/3 or x = 7 TalentJR · talentjr.in/quadratic-equations-worksheet
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Nature of roots Class 10 · Worksheet 3 · set 22
Name: Date: Score: / 8
Find the discriminant and the nature of the roots.
Nature of the roots of 3x² − 3x − 2 = 0 Nature of the roots of 5x² − 4x − 2 = 0 Nature of the roots of x² + 9x − 3 = 0 Nature of the roots of x² + x + 3 = 0 Nature of the roots of 2x² − 2 = 0 Nature of the roots of 4x² − 3x − 5 = 0 Nature of the roots of 5x² − 6x + 1 = 0 Nature of the roots of 4x² + 4x + 4 = 0
✅ Answer key — Nature of roots
D = 33 → two distinct real roots D = 56 → two distinct real roots D = 93 → two distinct real roots D = −11 → no real roots D = 16 → two distinct real roots D = 89 → two distinct real roots D = 16 → two distinct real roots D = −48 → no real roots TalentJR · talentjr.in/quadratic-equations-worksheet
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Quadratic formula Class 10 · Worksheet 4 · set 22
Name: Date: Score: / 6
Solve using the quadratic formula.
Solve by the quadratic formula: 2x² + 6x − 4 = 0 Solve by the quadratic formula: 2x² − x − 8 = 0 Solve by the quadratic formula: x² + 6x − 9 = 0 Solve by the quadratic formula: 2x² + 2x − 3 = 0 Solve by the quadratic formula: 3x² + 3x − 9 = 0 Solve by the quadratic formula: x² − x − 9 = 0
✅ Answer key — Quadratic formula
x = (−3 ± √17)/2 (≈ 0.56, −3.56) x = (1 ± √65)/4 (≈ 2.27, −1.77) x = −3 ± 3√2 (≈ 1.24, −7.24) x = (−1 ± √7)/2 (≈ 0.82, −1.82) x = (−1 ± √13)/2 (≈ 1.3, −2.3) x = (1 ± √37)/2 (≈ 3.54, −2.54) TalentJR · talentjr.in/quadratic-equations-worksheet
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Find k Class 10 · Worksheet 5 · set 22
Name: Date: Score: / 6
Solve.
Find k if x² − 2x + k = 0 has equal roots. Find k if x² + kx + 36 = 0 has equal roots. Find k if x² + 14x + k = 0 has equal roots. Find k if x² − 14x + k = 0 has equal roots. Find k if x² + 6x + k = 0 has equal roots. Find k if x² − 16x + k = 0 has equal roots.
✅ Answer key — Find k
k = 1 k = 12 or k = −12 k = 49 k = 49 k = 9 k = 64 TalentJR · talentjr.in/quadratic-equations-worksheet
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Word problems Class 10 · Worksheet 6 · set 22
Name: Date: Score: / 6
Form a quadratic equation and solve.
The sum of the squares of two consecutive positive integers is 421. Find the integers. The product of two consecutive positive integers is 110. Find the integers. The length of a rectangular park is 10 m more than its width. Its area is 119 sq m. Find its length and width. The product of two consecutive positive integers is 42. Find the integers. The sum of the squares of two consecutive positive integers is 481. Find the integers. The sum of the squares of two consecutive positive integers is 365. Find the integers.
✅ Answer key — Word problems
14 and 15 10 and 11 width 7 m, length 17 m 6 and 7 15 and 16 13 and 14 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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