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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
Name: Date: Score: / 10
Solve.
x² + 9x + 20 = 0 x² + 6x − 16 = 0 x² + 13x + 36 = 0 x² − 2x − 63 = 0 x² + 6x + 9 = 0 x² − 7x − 8 = 0 x² + 7x + 12 = 0 x² − 1 = 0 x² + x − 2 = 0 x² + 7x + 10 = 0
✅ Answer key — Solve by factorisation
x = −5 or x = −4 x = −8 or x = 2 x = −9 or x = −4 x = −7 or x = 9 x = −3 (equal roots) x = −1 or x = 8 x = −4 or x = −3 x = −1 or x = 1 x = −2 or x = 1 x = −5 or x = −2 TalentJR · talentjr.in/quadratic-equations-worksheet
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Factorisation (a ≠ 1) Class 10 · Worksheet 2
Name: Date: Score: / 8
Solve by splitting the middle term.
2x² + 3x − 20 = 0 5x² − 7x − 24 = 0 4x² − 41x + 45 = 0 5x² − 14x − 3 = 0 5x² + 46x + 48 = 0 4x² + 23x + 28 = 0 4x² + 13x − 12 = 0 5x² + 31x − 72 = 0
✅ Answer key — Factorisation (a ≠ 1)
x = −4 or x = 5/2 x = −8/5 or x = 3 x = 5/4 or x = 9 x = −1/5 or x = 3 x = −8 or x = −6/5 x = −4 or x = −7/4 x = −4 or x = 3/4 x = −8 or x = 9/5 TalentJR · talentjr.in/quadratic-equations-worksheet
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Nature of roots Class 10 · Worksheet 3
Name: Date: Score: / 8
Find the discriminant and the nature of the roots.
Nature of the roots of 5x² + 8 = 0 Nature of the roots of 2x² + x + 7 = 0 Nature of the roots of x² + 2x + 8 = 0 Nature of the roots of 4x² − 6x − 5 = 0 Nature of the roots of 2x² − 8x + 7 = 0 Nature of the roots of x² + 3x + 1 = 0 Nature of the roots of 3x² − 6x + 4 = 0 Nature of the roots of 2x² − 4x − 6 = 0
✅ Answer key — Nature of roots
D = −160 → no real roots D = −55 → no real roots D = −28 → no real roots D = 116 → two distinct real roots D = 8 → two distinct real roots D = 5 → two distinct real roots D = −12 → no real roots D = 64 → two distinct real roots TalentJR · talentjr.in/quadratic-equations-worksheet
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Quadratic formula Class 10 · Worksheet 4
Name: Date: Score: / 6
Solve using the quadratic formula.
Solve by the quadratic formula: 2x² − 3x − 7 = 0 Solve by the quadratic formula: 2x² − 4x − 1 = 0 Solve by the quadratic formula: 4x² + x − 9 = 0 Solve by the quadratic formula: 2x² − 7 = 0 Solve by the quadratic formula: x² + 9x − 7 = 0 Solve by the quadratic formula: 4x² + x − 8 = 0
✅ Answer key — Quadratic formula
x = (3 ± √65)/4 (≈ 2.77, −1.27) x = (2 ± √6)/2 (≈ 2.22, −0.22) x = (−1 ± √145)/8 (≈ 1.38, −1.63) x = (±√14)/2 (≈ 1.87, −1.87) x = (−9 ± √109)/2 (≈ 0.72, −9.72) x = (−1 ± √129)/8 (≈ 1.29, −1.54) TalentJR · talentjr.in/quadratic-equations-worksheet
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Find k Class 10 · Worksheet 5
Name: Date: Score: / 6
Solve.
Find k if x² + kx + 81 = 0 has equal roots. Find k if x² + kx + 1 = 0 has equal roots. Find k if x² − 10x + k = 0 has equal roots. Find k if x² + kx + 16 = 0 has equal roots. Find k if x² + 16x + k = 0 has equal roots. Find k if x² + kx + 64 = 0 has equal roots.
✅ Answer key — Find k
k = 18 or k = −18 k = 2 or k = −2 k = 25 k = 8 or k = −8 k = 64 k = 16 or k = −16 TalentJR · talentjr.in/quadratic-equations-worksheet
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Word problems Class 10 · Worksheet 6
Name: Date: Score: / 6
Form a quadratic equation and solve.
The product of two consecutive positive integers is 110. Find the integers. The length of a rectangular park is 2 m more than its width. Its area is 483 sq m. Find its length and width. The product of two consecutive positive integers is 342. Find the integers. The length of a rectangular park is 10 m more than its width. Its area is 75 sq m. Find its length and width. The product of two consecutive positive integers is 812. Find the integers. The length of a rectangular park is 1 m more than its width. Its area is 306 sq m. Find its length and width.
✅ Answer key — Word problems
10 and 11 width 21 m, length 23 m 18 and 19 width 5 m, length 15 m 28 and 29 width 17 m, length 18 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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