Free · Class 10 · 6 worksheets · answer keys · practise online · set 21
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 21
Name: Date: Score: / 10
Solve.
x² − 7x + 6 = 0 x² − 8x + 12 = 0 x² + 4x − 12 = 0 x² − 7x − 8 = 0 x² + 10x + 25 = 0 x² − 3x − 40 = 0 x² + 8x + 16 = 0 x² + 2x − 63 = 0 x² − 14x + 45 = 0 x² − 9 = 0
✅ Answer key — Solve by factorisation
x = 1 or x = 6 x = 2 or x = 6 x = −6 or x = 2 x = −1 or x = 8 x = −5 (equal roots) x = −5 or x = 8 x = −4 (equal roots) x = −9 or x = 7 x = 5 or x = 9 x = −3 or x = 3 TalentJR · talentjr.in/quadratic-equations-worksheet
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Factorisation (a ≠ 1) Class 10 · Worksheet 2 · set 21
Name: Date: Score: / 8
Solve by splitting the middle term.
5x² + 16x + 3 = 0 2x² − 9x − 5 = 0 3x² + 10x − 48 = 0 5x² + 18x + 16 = 0 2x² + 7x + 5 = 0 5x² + 39x + 54 = 0 5x² + 16x + 12 = 0 5x² − 9x − 18 = 0
✅ Answer key — Factorisation (a ≠ 1)
x = −3 or x = −1/5 x = −1/2 or x = 5 x = −6 or x = 8/3 x = −2 or x = −8/5 x = −5/2 or x = −1 x = −6 or x = −9/5 x = −2 or x = −6/5 x = −6/5 or x = 3 TalentJR · talentjr.in/quadratic-equations-worksheet
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Nature of roots Class 10 · Worksheet 3 · set 21
Name: Date: Score: / 8
Find the discriminant and the nature of the roots.
Nature of the roots of 4x² + 8x − 9 = 0 Nature of the roots of 3x² − 3x + 6 = 0 Nature of the roots of x² − 3x + 5 = 0 Nature of the roots of x² − 6x − 6 = 0 Nature of the roots of 3x² + 2x + 7 = 0 Nature of the roots of 4x² − 9x + 2 = 0 Nature of the roots of 5x² − 6x − 9 = 0 Nature of the roots of 2x² − 4x + 5 = 0
✅ Answer key — Nature of roots
D = 208 → two distinct real roots D = −63 → no real roots D = −11 → no real roots D = 60 → two distinct real roots D = −80 → no real roots D = 49 → two distinct real roots D = 216 → two distinct real roots D = −24 → no real roots TalentJR · talentjr.in/quadratic-equations-worksheet
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Quadratic formula Class 10 · Worksheet 4 · set 21
Name: Date: Score: / 6
Solve using the quadratic formula.
Solve by the quadratic formula: 2x² − 8x + 4 = 0 Solve by the quadratic formula: x² − 7x + 2 = 0 Solve by the quadratic formula: x² + 6x + 4 = 0 Solve by the quadratic formula: 2x² + 7x − 2 = 0 Solve by the quadratic formula: 3x² − x − 7 = 0 Solve by the quadratic formula: 4x² + 6x − 9 = 0
✅ Answer key — Quadratic formula
x = 2 ± √2 (≈ 3.41, 0.59) x = (7 ± √41)/2 (≈ 6.7, 0.3) x = −3 ± √5 (≈ −0.76, −5.24) x = (−7 ± √65)/4 (≈ 0.27, −3.77) x = (1 ± √85)/6 (≈ 1.7, −1.37) x = (−3 ± 3√5)/4 (≈ 0.93, −2.43) TalentJR · talentjr.in/quadratic-equations-worksheet
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Find k Class 10 · Worksheet 5 · set 21
Name: Date: Score: / 6
Solve.
Find k if x² + 6x + k = 0 has equal roots. Find k if x² + kx + 9 = 0 has equal roots. Find k if x² − 14x + k = 0 has equal roots. Find k if x² + kx + 25 = 0 has equal roots. Find k if x² + 4x + k = 0 has equal roots. Find k if x² + kx + 64 = 0 has equal roots.
✅ Answer key — Find k
k = 9 k = 6 or k = −6 k = 49 k = 10 or k = −10 k = 4 k = 16 or k = −16 TalentJR · talentjr.in/quadratic-equations-worksheet
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Word problems Class 10 · Worksheet 6 · set 21
Name: Date: Score: / 6
Form a quadratic equation and solve.
The length of a rectangular park is 6 m more than its width. Its area is 432 sq m. Find its length and width. The product of two consecutive positive integers is 90. Find the integers. The length of a rectangular park is 5 m more than its width. Its area is 126 sq m. Find its length and width. The product of two consecutive positive integers is 600. Find the integers. The length of a rectangular park is 6 m more than its width. Its area is 520 sq m. Find its length and width. The product of two consecutive positive integers is 182. Find the integers.
✅ Answer key — Word problems
width 18 m, length 24 m 9 and 10 width 9 m, length 14 m 24 and 25 width 20 m, length 26 m 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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