Free · Class 10 · 6 worksheets · answer keys · practise online · set 6
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 6
Name: Date: Score: / 10
Solve.
x² − 3x − 54 = 0 x² − 3x − 10 = 0 x² − 9 = 0 x² − 16x + 64 = 0 x² + 8x + 12 = 0 x² + x − 30 = 0 x² − x − 42 = 0 x² + 13x + 40 = 0 x² + 3x − 10 = 0 x² + 6x − 27 = 0
✅ Answer key — Solve by factorisation
x = −6 or x = 9 x = −2 or x = 5 x = −3 or x = 3 x = 8 (equal roots) x = −6 or x = −2 x = −6 or x = 5 x = −6 or x = 7 x = −8 or x = −5 x = −5 or x = 2 x = −9 or x = 3 TalentJR · talentjr.in/quadratic-equations-worksheet
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Factorisation (a ≠ 1) Class 10 · Worksheet 2 · set 6
Name: Date: Score: / 8
Solve by splitting the middle term.
2x² − 13x + 18 = 0 3x² − x − 14 = 0 5x² + 22x + 21 = 0 2x² + 17x + 21 = 0 5x² − 32x + 12 = 0 4x² − 25x + 25 = 0 4x² − 9x − 9 = 0 4x² − 11x − 45 = 0
✅ Answer key — Factorisation (a ≠ 1)
x = 2 or x = 9/2 x = −2 or x = 7/3 x = −3 or x = −7/5 x = −7 or x = −3/2 x = 2/5 or x = 6 x = 5/4 or x = 5 x = −3/4 or x = 3 x = −9/4 or x = 5 TalentJR · talentjr.in/quadratic-equations-worksheet
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Nature of roots Class 10 · Worksheet 3 · set 6
Name: Date: Score: / 8
Find the discriminant and the nature of the roots.
Nature of the roots of 4x² − x − 1 = 0 Nature of the roots of x² + 4x + 5 = 0 Nature of the roots of 5x² + 7x + 2 = 0 Nature of the roots of 4x² − 3x − 5 = 0 Nature of the roots of x² + 8x + 1 = 0 Nature of the roots of 3x² − 8 = 0 Nature of the roots of 2x² − 7x − 4 = 0 Nature of the roots of x² − 6x − 1 = 0
✅ Answer key — Nature of roots
D = 17 → two distinct real roots D = −4 → no real roots D = 9 → two distinct real roots D = 89 → two distinct real roots D = 60 → two distinct real roots D = 96 → two distinct real roots D = 81 → two distinct real roots D = 40 → two distinct real roots TalentJR · talentjr.in/quadratic-equations-worksheet
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Quadratic formula Class 10 · Worksheet 4 · set 6
Name: Date: Score: / 6
Solve using the quadratic formula.
Solve by the quadratic formula: 4x² + 5x − 4 = 0 Solve by the quadratic formula: 3x² + 7x − 1 = 0 Solve by the quadratic formula: 3x² + 5x − 4 = 0 Solve by the quadratic formula: x² + 8x − 7 = 0 Solve by the quadratic formula: x² + x − 5 = 0 Solve by the quadratic formula: x² + 8x + 6 = 0
✅ Answer key — Quadratic formula
x = (−5 ± √89)/8 (≈ 0.55, −1.8) x = (−7 ± √61)/6 (≈ 0.14, −2.47) x = (−5 ± √73)/6 (≈ 0.59, −2.26) x = −4 ± √23 (≈ 0.8, −8.8) x = (−1 ± √21)/2 (≈ 1.79, −2.79) x = −4 ± √10 (≈ −0.84, −7.16) TalentJR · talentjr.in/quadratic-equations-worksheet
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Find k Class 10 · Worksheet 5 · set 6
Name: Date: Score: / 6
Solve.
Find k if x² − 12x + k = 0 has equal roots. Find k if x² + 2x + k = 0 has equal roots. Find k if x² − 8x + k = 0 has equal roots. Find k if x² + kx + 81 = 0 has equal roots. Find k if x² + 18x + k = 0 has equal roots. Find k if x² + kx + 9 = 0 has equal roots.
✅ Answer key — Find k
k = 36 k = 1 k = 16 k = 18 or k = −18 k = 81 k = 6 or k = −6 TalentJR · talentjr.in/quadratic-equations-worksheet
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Word problems Class 10 · Worksheet 6 · set 6
Name: Date: Score: / 6
Form a quadratic equation and solve.
The length of a rectangular park is 9 m more than its width. Its area is 136 sq m. Find its length and width. The sum of the squares of two consecutive positive integers is 313. Find the integers. The sum of the squares of two consecutive positive integers is 761. Find the integers. The sum of the squares of two consecutive positive integers is 365. Find the integers. The sum of the squares of two consecutive positive integers is 481. Find the integers. The length of a rectangular park is 10 m more than its width. Its area is 375 sq m. Find its length and width.
✅ Answer key — Word problems
width 8 m, length 17 m 12 and 13 19 and 20 13 and 14 15 and 16 width 15 m, length 25 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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