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 − 7x + 12 = 0.
7 · 12 · 0 · Factored quadratic equations
2. Find the greater root of x² − 14x + 13 = 0.
14 · 13 · 0 · Factored quadratic equations
3. Find the greater root of x² − 18x + 45 = 0.
18 · 45 · 0 · Factored quadratic equations
4. Find the greater root of x² − 15x + 50 = 0.
15 · 50 · 0 · Factored quadratic equations
5. Find the greater root of x² − 15x + 26 = 0.
15 · 26 · 0 · Factored quadratic equations
6. Find the greater root of x² − 3x + 2 = 0.
3 · 2 · 0 · Factored quadratic equations
7. Find the greater root of x² − 16x + 63 = 0.
16 · 63 · 0 · Factored quadratic equations
8. Find the greater root of x² − 5x + 4 = 0.
5 · 4 · 0 · Factored quadratic equations
9. Find the greater root of x² − 20x + 91 = 0.
20 · 91 · 0 · Factored quadratic equations
10. Find the greater root of x² − 14x + 48 = 0.
14 · 48 · 0 · Factored quadratic equations
11. Find the greater root of x² − 11x + 18 = 0.
11 · 18 · 0 · Factored quadratic equations
12. Find the greater root of x² − 17x + 70 = 0.
17 · 70 · 0 · Factored quadratic equations
12 questions · Seed 55 · 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 − 7x + 12 = 0.
4 Factorise into (x − 3)(x − 4) = 0. The roots are 3 and 4, so the greater root is 4.
2. 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.
3. Find the greater root of x² − 18x + 45 = 0.
15 Factorise into (x − 3)(x − 15) = 0. The roots are 3 and 15, so the greater root is 15.
4. Find the greater root of x² − 15x + 50 = 0.
10 Factorise into (x − 5)(x − 10) = 0. The roots are 5 and 10, so the greater root is 10.
5. 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.
6. 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.
7. 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.
8. Find the greater root of x² − 5x + 4 = 0.
4 Factorise into (x − 1)(x − 4) = 0. The roots are 1 and 4, so the greater root is 4.
9. Find the greater root of x² − 20x + 91 = 0.
13 Factorise into (x − 7)(x − 13) = 0. The roots are 7 and 13, so the greater root is 13.
10. Find the greater root of x² − 14x + 48 = 0.
8 Factorise into (x − 6)(x − 8) = 0. The roots are 6 and 8, so the greater root is 8.
11. Find the greater root of x² − 11x + 18 = 0.
9 Factorise into (x − 2)(x − 9) = 0. The roots are 2 and 9, so the greater root is 9.
12. Find the greater root of x² − 17x + 70 = 0.
10 Factorise into (x − 7)(x − 10) = 0. The roots are 7 and 10, so the greater root is 10.
12 questions · Seed 55 · 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 − 7x + 12 = 0.
7 · 12 · 0 · Factored quadratic equations
2. Find the greater root of x² − 14x + 13 = 0.
14 · 13 · 0 · Factored quadratic equations
3. Find the greater root of x² − 18x + 45 = 0.
18 · 45 · 0 · Factored quadratic equations
4. Find the greater root of x² − 15x + 50 = 0.
15 · 50 · 0 · Factored quadratic equations
5. Find the greater root of x² − 15x + 26 = 0.
15 · 26 · 0 · Factored quadratic equations
6. Find the greater root of x² − 3x + 2 = 0.
3 · 2 · 0 · Factored quadratic equations
7. Find the greater root of x² − 16x + 63 = 0.
16 · 63 · 0 · Factored quadratic equations
8. Find the greater root of x² − 5x + 4 = 0.
5 · 4 · 0 · Factored quadratic equations
9. Find the greater root of x² − 20x + 91 = 0.
20 · 91 · 0 · Factored quadratic equations
10. Find the greater root of x² − 14x + 48 = 0.
14 · 48 · 0 · Factored quadratic equations
11. Find the greater root of x² − 11x + 18 = 0.
11 · 18 · 0 · Factored quadratic equations
12. Find the greater root of x² − 17x + 70 = 0.
17 · 70 · 0 · Factored quadratic equations
12 questions · Seed 55 · 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 − 7x + 12 = 0.
4 Factorise into (x − 3)(x − 4) = 0. The roots are 3 and 4, so the greater root is 4.
2. 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.
3. Find the greater root of x² − 18x + 45 = 0.
15 Factorise into (x − 3)(x − 15) = 0. The roots are 3 and 15, so the greater root is 15.
4. Find the greater root of x² − 15x + 50 = 0.
10 Factorise into (x − 5)(x − 10) = 0. The roots are 5 and 10, so the greater root is 10.
5. 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.
6. 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.
7. 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.
8. Find the greater root of x² − 5x + 4 = 0.
4 Factorise into (x − 1)(x − 4) = 0. The roots are 1 and 4, so the greater root is 4.
9. Find the greater root of x² − 20x + 91 = 0.
13 Factorise into (x − 7)(x − 13) = 0. The roots are 7 and 13, so the greater root is 13.
10. Find the greater root of x² − 14x + 48 = 0.
8 Factorise into (x − 6)(x − 8) = 0. The roots are 6 and 8, so the greater root is 8.
11. Find the greater root of x² − 11x + 18 = 0.
9 Factorise into (x − 2)(x − 9) = 0. The roots are 2 and 9, so the greater root is 9.
12. Find the greater root of x² − 17x + 70 = 0.
10 Factorise into (x − 7)(x − 10) = 0. The roots are 7 and 10, so the greater root is 10.
12 questions · Seed 55 · Age guidance, not curriculum certification
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