Back to worksheets Maths Ages 13-15
Factored quadratic equations Solve a monic quadratic equation by factorising into two linear brackets and identifying the greater root. Review suitability for your learners before teaching.
Student worksheet Answer key
Worksheet Studio Practice pack · Ages 13-15
Factored quadratic equations Take your time. Show your thinking.
1. Find the greater root of x² − 12x + 35 = 0.
12 · 35 · 0 · Factored quadratic equations
2. Find the greater root of x² − 14x + 40 = 0.
14 · 40 · 0 · Factored quadratic equations
3. Find the greater root of x² − 18x + 65 = 0.
18 · 65 · 0 · Factored quadratic equations
4. Find the greater root of x² − 16x + 63 = 0.
16 · 63 · 0 · Factored quadratic equations
5. Find the greater root of x² − 3x + 2 = 0.
3 · 2 · 0 · Factored quadratic equations
6. Find the greater root of x² − 15x + 36 = 0.
15 · 36 · 0 · Factored quadratic equations
7. Find the greater root of x² − 22x + 112 = 0.
22 · 112 · 0 · Factored quadratic equations
8. Find the greater root of x² − 21x + 104 = 0.
21 · 104 · 0 · Factored quadratic equations
9. Find the greater root of x² − 8x + 7 = 0.
8 · 7 · 0 · Factored quadratic equations
10. Find the greater root of x² − 21x + 90 = 0.
21 · 90 · 0 · Factored quadratic equations
11. Find the greater root of x² − 15x + 26 = 0.
15 · 26 · 0 · Factored quadratic equations
12. Find the greater root of x² − 14x + 13 = 0.
14 · 13 · 0 · Factored quadratic equations
12 questions · Seed 46 · Age guidance, not curriculum certification
View the answer key Worksheet Studio Answer key · Ages 13-15
Factored quadratic equations Answers and reasoning. Review before teaching.
1. Find the greater root of x² − 12x + 35 = 0.
7 Factorise into (x − 5)(x − 7) = 0. The roots are 5 and 7, so the greater root is 7.
2. Find the greater root of x² − 14x + 40 = 0.
10 Factorise into (x − 4)(x − 10) = 0. The roots are 4 and 10, so the greater root is 10.
3. Find the greater root of x² − 18x + 65 = 0.
13 Factorise into (x − 5)(x − 13) = 0. The roots are 5 and 13, so the greater root is 13.
4. Find the greater root of x² − 16x + 63 = 0.
9 Factorise into (x − 7)(x − 9) = 0. The roots are 7 and 9, so the greater root is 9.
5. Find the greater root of x² − 3x + 2 = 0.
2 Factorise into (x − 1)(x − 2) = 0. The roots are 1 and 2, so the greater root is 2.
6. Find the greater root of x² − 15x + 36 = 0.
12 Factorise into (x − 3)(x − 12) = 0. The roots are 3 and 12, so the greater root is 12.
7. Find the greater root of x² − 22x + 112 = 0.
14 Factorise into (x − 8)(x − 14) = 0. The roots are 8 and 14, so the greater root is 14.
8. Find the greater root of x² − 21x + 104 = 0.
13 Factorise into (x − 8)(x − 13) = 0. The roots are 8 and 13, so the greater root is 13.
9. Find the greater root of x² − 8x + 7 = 0.
7 Factorise into (x − 1)(x − 7) = 0. The roots are 1 and 7, so the greater root is 7.
10. Find the greater root of x² − 21x + 90 = 0.
15 Factorise into (x − 6)(x − 15) = 0. The roots are 6 and 15, so the greater root is 15.
11. Find the greater root of x² − 15x + 26 = 0.
13 Factorise into (x − 2)(x − 13) = 0. The roots are 2 and 13, so the greater root is 13.
12. Find the greater root of x² − 14x + 13 = 0.
13 Factorise into (x − 1)(x − 13) = 0. The roots are 1 and 13, so the greater root is 13.
12 questions · Seed 46 · Age guidance, not curriculum certification
Worksheet Studio Practice pack · Ages 13-15
Factored quadratic equations Take your time. Show your thinking.
1. Find the greater root of x² − 12x + 35 = 0.
12 · 35 · 0 · Factored quadratic equations
2. Find the greater root of x² − 14x + 40 = 0.
14 · 40 · 0 · Factored quadratic equations
3. Find the greater root of x² − 18x + 65 = 0.
18 · 65 · 0 · Factored quadratic equations
4. Find the greater root of x² − 16x + 63 = 0.
16 · 63 · 0 · Factored quadratic equations
5. Find the greater root of x² − 3x + 2 = 0.
3 · 2 · 0 · Factored quadratic equations
6. Find the greater root of x² − 15x + 36 = 0.
15 · 36 · 0 · Factored quadratic equations
7. Find the greater root of x² − 22x + 112 = 0.
22 · 112 · 0 · Factored quadratic equations
8. Find the greater root of x² − 21x + 104 = 0.
21 · 104 · 0 · Factored quadratic equations
9. Find the greater root of x² − 8x + 7 = 0.
8 · 7 · 0 · Factored quadratic equations
10. Find the greater root of x² − 21x + 90 = 0.
21 · 90 · 0 · Factored quadratic equations
11. Find the greater root of x² − 15x + 26 = 0.
15 · 26 · 0 · Factored quadratic equations
12. Find the greater root of x² − 14x + 13 = 0.
14 · 13 · 0 · Factored quadratic equations
12 questions · Seed 46 · Age guidance, not curriculum certification
Worksheet Studio Answer key · Ages 13-15
Factored quadratic equations Answers and reasoning. Review before teaching.
1. Find the greater root of x² − 12x + 35 = 0.
7 Factorise into (x − 5)(x − 7) = 0. The roots are 5 and 7, so the greater root is 7.
2. Find the greater root of x² − 14x + 40 = 0.
10 Factorise into (x − 4)(x − 10) = 0. The roots are 4 and 10, so the greater root is 10.
3. Find the greater root of x² − 18x + 65 = 0.
13 Factorise into (x − 5)(x − 13) = 0. The roots are 5 and 13, so the greater root is 13.
4. Find the greater root of x² − 16x + 63 = 0.
9 Factorise into (x − 7)(x − 9) = 0. The roots are 7 and 9, so the greater root is 9.
5. Find the greater root of x² − 3x + 2 = 0.
2 Factorise into (x − 1)(x − 2) = 0. The roots are 1 and 2, so the greater root is 2.
6. Find the greater root of x² − 15x + 36 = 0.
12 Factorise into (x − 3)(x − 12) = 0. The roots are 3 and 12, so the greater root is 12.
7. Find the greater root of x² − 22x + 112 = 0.
14 Factorise into (x − 8)(x − 14) = 0. The roots are 8 and 14, so the greater root is 14.
8. Find the greater root of x² − 21x + 104 = 0.
13 Factorise into (x − 8)(x − 13) = 0. The roots are 8 and 13, so the greater root is 13.
9. Find the greater root of x² − 8x + 7 = 0.
7 Factorise into (x − 1)(x − 7) = 0. The roots are 1 and 7, so the greater root is 7.
10. Find the greater root of x² − 21x + 90 = 0.
15 Factorise into (x − 6)(x − 15) = 0. The roots are 6 and 15, so the greater root is 15.
11. Find the greater root of x² − 15x + 26 = 0.
13 Factorise into (x − 2)(x − 13) = 0. The roots are 2 and 13, so the greater root is 13.
12. Find the greater root of x² − 14x + 13 = 0.
13 Factorise into (x − 1)(x − 13) = 0. The roots are 1 and 13, so the greater root is 13.
12 questions · Seed 46 · Age guidance, not curriculum certification
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