Free · Class 10 · 6 worksheets · answer keys · practise online · set 7
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 7
Name: Date: Score: / 10
Solve.
x² − 15x + 54 = 0 x² + 3x − 18 = 0 x² + 12x + 32 = 0 x² − 2x − 8 = 0 x² + 4x − 45 = 0 x² + 6x − 16 = 0 x² − 10x + 16 = 0 x² + x − 12 = 0 x² + 8x − 9 = 0 x² + 4x + 4 = 0
✅ Answer key — Solve by factorisation
x = 6 or x = 9 x = −6 or x = 3 x = −8 or x = −4 x = −2 or x = 4 x = −9 or x = 5 x = −8 or x = 2 x = 2 or x = 8 x = −4 or x = 3 x = −9 or x = 1 x = −2 (equal roots) TalentJR · talentjr.in/quadratic-equations-worksheet
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Factorisation (a ≠ 1) Class 10 · Worksheet 2 · set 7
Name: Date: Score: / 8
Solve by splitting the middle term.
2x² − 21x + 27 = 0 5x² − 4x − 12 = 0 4x² − 11x − 20 = 0 4x² − 35x + 24 = 0 3x² + 5x − 12 = 0 3x² + 19x + 28 = 0 4x² + 7x + 3 = 0 3x² + 8x − 16 = 0
✅ Answer key — Factorisation (a ≠ 1)
x = 3/2 or x = 9 x = −6/5 or x = 2 x = −5/4 or x = 4 x = 3/4 or x = 8 x = −3 or x = 4/3 x = −4 or x = −7/3 x = −1 or x = −3/4 x = −4 or x = 4/3 TalentJR · talentjr.in/quadratic-equations-worksheet
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Nature of roots Class 10 · Worksheet 3 · set 7
Name: Date: Score: / 8
Find the discriminant and the nature of the roots.
Nature of the roots of x² + 5x − 1 = 0 Nature of the roots of x² + 5x − 2 = 0 Nature of the roots of 5x² + 6x − 6 = 0 Nature of the roots of 2x² − 6x + 6 = 0 Nature of the roots of 2x² − 2x − 6 = 0 Nature of the roots of 3x² + 4x − 4 = 0 Nature of the roots of 2x² + 7x + 1 = 0 Nature of the roots of x² + 8x + 8 = 0
✅ Answer key — Nature of roots
D = 29 → two distinct real roots D = 33 → two distinct real roots D = 156 → two distinct real roots D = −12 → no real roots D = 52 → two distinct real roots D = 64 → two distinct real roots D = 41 → two distinct real roots D = 32 → two distinct real roots TalentJR · talentjr.in/quadratic-equations-worksheet
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Quadratic formula Class 10 · Worksheet 4 · set 7
Name: Date: Score: / 6
Solve using the quadratic formula.
Solve by the quadratic formula: 3x² + x − 9 = 0 Solve by the quadratic formula: 2x² + 9x − 9 = 0 Solve by the quadratic formula: 3x² + 4x − 1 = 0 Solve by the quadratic formula: 3x² − 8x − 2 = 0 Solve by the quadratic formula: x² + 3x + 1 = 0 Solve by the quadratic formula: x² − 6x − 3 = 0
✅ Answer key — Quadratic formula
x = (−1 ± √109)/6 (≈ 1.57, −1.91) x = (−9 ± 3√17)/4 (≈ 0.84, −5.34) x = (−2 ± √7)/3 (≈ 0.22, −1.55) x = (4 ± √22)/3 (≈ 2.9, −0.23) x = (−3 ± √5)/2 (≈ −0.38, −2.62) x = 3 ± 2√3 (≈ 6.46, −0.46) TalentJR · talentjr.in/quadratic-equations-worksheet
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Find k Class 10 · Worksheet 5 · set 7
Name: Date: Score: / 6
Solve.
Find k if x² + kx + 1 = 0 has equal roots. Find k if x² + 4x + k = 0 has equal roots. Find k if x² + kx + 9 = 0 has equal roots. Find k if x² + kx + 4 = 0 has equal roots. Find k if x² + 8x + k = 0 has equal roots. Find k if x² + kx + 16 = 0 has equal roots.
✅ Answer key — Find k
k = 2 or k = −2 k = 4 k = 6 or k = −6 k = 4 or k = −4 k = 16 k = 8 or k = −8 TalentJR · talentjr.in/quadratic-equations-worksheet
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Word problems Class 10 · Worksheet 6 · set 7
Name: Date: Score: / 6
Form a quadratic equation and solve.
The sum of the squares of two consecutive positive integers is 365. Find the integers. The product of two consecutive positive integers is 600. Find the integers. The sum of the squares of two consecutive positive integers is 221. Find the integers. The length of a rectangular park is 7 m more than its width. Its area is 44 sq m. Find its length and width. The length of a rectangular park is 6 m more than its width. Its area is 216 sq m. Find its length and width. The length of a rectangular park is 2 m more than its width. Its area is 624 sq m. Find its length and width.
✅ Answer key — Word problems
13 and 14 24 and 25 10 and 11 width 4 m, length 11 m width 12 m, length 18 m width 24 m, length 26 m 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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