Free · Class 10 · 6 worksheets · answer keys · practise online · set 12
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 12
Name: Date: Score: / 10
Solve.
x² − 4x − 32 = 0 x² − x − 6 = 0 x² − 6x + 5 = 0 x² − 8x − 9 = 0 x² + 6x − 16 = 0 x² − 9 = 0 x² − 9x + 20 = 0 x² − 6x − 7 = 0 x² + 4x − 5 = 0 x² − 14x + 45 = 0
✅ Answer key — Solve by factorisation
x = −4 or x = 8 x = −2 or x = 3 x = 1 or x = 5 x = −1 or x = 9 x = −8 or x = 2 x = −3 or x = 3 x = 4 or x = 5 x = −1 or x = 7 x = −5 or x = 1 x = 5 or x = 9 TalentJR · talentjr.in/quadratic-equations-worksheet
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Factorisation (a ≠ 1) Class 10 · Worksheet 2 · set 12
Name: Date: Score: / 8
Solve by splitting the middle term.
5x² − 27x + 28 = 0 3x² − 26x + 48 = 0 4x² − 21x − 49 = 0 5x² + 31x − 28 = 0 3x² − x − 4 = 0 5x² − 12x + 4 = 0 2x² − 5x − 63 = 0 5x² − 4x − 9 = 0
✅ Answer key — Factorisation (a ≠ 1)
x = 7/5 or x = 4 x = 8/3 or x = 6 x = −7/4 or x = 7 x = −7 or x = 4/5 x = −1 or x = 4/3 x = 2/5 or x = 2 x = −9/2 or x = 7 x = −1 or x = 9/5 TalentJR · talentjr.in/quadratic-equations-worksheet
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Nature of roots Class 10 · Worksheet 3 · set 12
Name: Date: Score: / 8
Find the discriminant and the nature of the roots.
Nature of the roots of 5x² + 3x − 4 = 0 Nature of the roots of 3x² + 7x + 6 = 0 Nature of the roots of 2x² + 2x + 5 = 0 Nature of the roots of 2x² + 8x + 7 = 0 Nature of the roots of 4x² + 3x + 8 = 0 Nature of the roots of 2x² − x − 6 = 0 Nature of the roots of 2x² + x − 6 = 0 Nature of the roots of 3x² + 4x + 3 = 0
✅ Answer key — Nature of roots
D = 89 → two distinct real roots D = −23 → no real roots D = −36 → no real roots D = 8 → two distinct real roots D = −119 → no real roots D = 49 → two distinct real roots D = 49 → two distinct real roots D = −20 → no real roots TalentJR · talentjr.in/quadratic-equations-worksheet
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Quadratic formula Class 10 · Worksheet 4 · set 12
Name: Date: Score: / 6
Solve using the quadratic formula.
Solve by the quadratic formula: 4x² + 9x − 7 = 0 Solve by the quadratic formula: 3x² + 3x − 7 = 0 Solve by the quadratic formula: 3x² − 8x − 4 = 0 Solve by the quadratic formula: 3x² + 7x − 5 = 0 Solve by the quadratic formula: 2x² − 7 = 0 Solve by the quadratic formula: x² + 2x − 5 = 0
✅ Answer key — Quadratic formula
x = (−9 ± √193)/8 (≈ 0.61, −2.86) x = (−3 ± √93)/6 (≈ 1.11, −2.11) x = (4 ± 2√7)/3 (≈ 3.1, −0.43) x = (−7 ± √109)/6 (≈ 0.57, −2.91) x = (±√14)/2 (≈ 1.87, −1.87) x = −1 ± √6 (≈ 1.45, −3.45) TalentJR · talentjr.in/quadratic-equations-worksheet
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Find k Class 10 · Worksheet 5 · set 12
Name: Date: Score: / 6
Solve.
Find k if x² − 8x + k = 0 has equal roots. Find k if x² − 14x + k = 0 has equal roots. Find k if x² + kx + 64 = 0 has equal roots. Find k if x² − 18x + k = 0 has equal roots. Find k if x² − 12x + k = 0 has equal roots. Find k if x² + kx + 25 = 0 has equal roots.
✅ Answer key — Find k
k = 16 k = 49 k = 16 or k = −16 k = 81 k = 36 k = 10 or k = −10 TalentJR · talentjr.in/quadratic-equations-worksheet
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Word problems Class 10 · Worksheet 6 · set 12
Name: Date: Score: / 6
Form a quadratic equation and solve.
The length of a rectangular park is 5 m more than its width. Its area is 750 sq m. Find its length and width. The length of a rectangular park is 10 m more than its width. Its area is 144 sq m. Find its length and width. The length of a rectangular park is 5 m more than its width. Its area is 696 sq m. Find its length and width. The product of two consecutive positive integers is 870. Find the integers. The length of a rectangular park is 1 m more than its width. Its area is 90 sq m. Find its length and width. The product of two consecutive positive integers is 132. Find the integers.
✅ Answer key — Word problems
width 25 m, length 30 m width 8 m, length 18 m width 24 m, length 29 m 29 and 30 width 9 m, length 10 m 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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