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 − 18x + 72 = 0.
18 · 72 · 0 · Factored quadratic equations
2. Find the greater root of x² − 12x + 35 = 0.
12 · 35 · 0 · Factored quadratic equations
3. Find the greater root of x² − 17x + 70 = 0.
17 · 70 · 0 · Factored quadratic equations
4. Find the greater root of x² − 16x + 55 = 0.
16 · 55 · 0 · Factored quadratic equations
5. Find the greater root of x² − 15x + 44 = 0.
15 · 44 · 0 · Factored quadratic equations
6. Find the greater root of x² − 11x + 24 = 0.
11 · 24 · 0 · Factored quadratic equations
7. Find the greater root of x² − 9x + 20 = 0.
9 · 20 · 0 · Factored quadratic equations
8. Find the greater root of x² − 20x + 96 = 0.
20 · 96 · 0 · Factored quadratic equations
9. Find the greater root of x² − 17x + 42 = 0.
17 · 42 · 0 · Factored quadratic equations
10. Find the greater root of x² − 11x + 30 = 0.
11 · 30 · 0 · Factored quadratic equations
11. Find the greater root of x² − 20x + 84 = 0.
20 · 84 · 0 · Factored quadratic equations
12. Find the greater root of x² − 15x + 56 = 0.
15 · 56 · 0 · Factored quadratic equations
12 questions · Seed 43 · 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 − 18x + 72 = 0.
12 Factorise into (x − 6)(x − 12) = 0. The roots are 6 and 12, so the greater root is 12.
2. 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.
3. 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.
4. Find the greater root of x² − 16x + 55 = 0.
11 Factorise into (x − 5)(x − 11) = 0. The roots are 5 and 11, so the greater root is 11.
5. Find the greater root of x² − 15x + 44 = 0.
11 Factorise into (x − 4)(x − 11) = 0. The roots are 4 and 11, so the greater root is 11.
6. Find the greater root of x² − 11x + 24 = 0.
8 Factorise into (x − 3)(x − 8) = 0. The roots are 3 and 8, so the greater root is 8.
7. Find the greater root of x² − 9x + 20 = 0.
5 Factorise into (x − 4)(x − 5) = 0. The roots are 4 and 5, so the greater root is 5.
8. Find the greater root of x² − 20x + 96 = 0.
12 Factorise into (x − 8)(x − 12) = 0. The roots are 8 and 12, so the greater root is 12.
9. Find the greater root of x² − 17x + 42 = 0.
14 Factorise into (x − 3)(x − 14) = 0. The roots are 3 and 14, so the greater root is 14.
10. Find the greater root of x² − 11x + 30 = 0.
6 Factorise into (x − 5)(x − 6) = 0. The roots are 5 and 6, so the greater root is 6.
11. Find the greater root of x² − 20x + 84 = 0.
14 Factorise into (x − 6)(x − 14) = 0. The roots are 6 and 14, so the greater root is 14.
12. Find the greater root of x² − 15x + 56 = 0.
8 Factorise into (x − 7)(x − 8) = 0. The roots are 7 and 8, so the greater root is 8.
12 questions · Seed 43 · 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 − 18x + 72 = 0.
18 · 72 · 0 · Factored quadratic equations
2. Find the greater root of x² − 12x + 35 = 0.
12 · 35 · 0 · Factored quadratic equations
3. Find the greater root of x² − 17x + 70 = 0.
17 · 70 · 0 · Factored quadratic equations
4. Find the greater root of x² − 16x + 55 = 0.
16 · 55 · 0 · Factored quadratic equations
5. Find the greater root of x² − 15x + 44 = 0.
15 · 44 · 0 · Factored quadratic equations
6. Find the greater root of x² − 11x + 24 = 0.
11 · 24 · 0 · Factored quadratic equations
7. Find the greater root of x² − 9x + 20 = 0.
9 · 20 · 0 · Factored quadratic equations
8. Find the greater root of x² − 20x + 96 = 0.
20 · 96 · 0 · Factored quadratic equations
9. Find the greater root of x² − 17x + 42 = 0.
17 · 42 · 0 · Factored quadratic equations
10. Find the greater root of x² − 11x + 30 = 0.
11 · 30 · 0 · Factored quadratic equations
11. Find the greater root of x² − 20x + 84 = 0.
20 · 84 · 0 · Factored quadratic equations
12. Find the greater root of x² − 15x + 56 = 0.
15 · 56 · 0 · Factored quadratic equations
12 questions · Seed 43 · 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 − 18x + 72 = 0.
12 Factorise into (x − 6)(x − 12) = 0. The roots are 6 and 12, so the greater root is 12.
2. 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.
3. 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.
4. Find the greater root of x² − 16x + 55 = 0.
11 Factorise into (x − 5)(x − 11) = 0. The roots are 5 and 11, so the greater root is 11.
5. Find the greater root of x² − 15x + 44 = 0.
11 Factorise into (x − 4)(x − 11) = 0. The roots are 4 and 11, so the greater root is 11.
6. Find the greater root of x² − 11x + 24 = 0.
8 Factorise into (x − 3)(x − 8) = 0. The roots are 3 and 8, so the greater root is 8.
7. Find the greater root of x² − 9x + 20 = 0.
5 Factorise into (x − 4)(x − 5) = 0. The roots are 4 and 5, so the greater root is 5.
8. Find the greater root of x² − 20x + 96 = 0.
12 Factorise into (x − 8)(x − 12) = 0. The roots are 8 and 12, so the greater root is 12.
9. Find the greater root of x² − 17x + 42 = 0.
14 Factorise into (x − 3)(x − 14) = 0. The roots are 3 and 14, so the greater root is 14.
10. Find the greater root of x² − 11x + 30 = 0.
6 Factorise into (x − 5)(x − 6) = 0. The roots are 5 and 6, so the greater root is 6.
11. Find the greater root of x² − 20x + 84 = 0.
14 Factorise into (x − 6)(x − 14) = 0. The roots are 6 and 14, so the greater root is 14.
12. Find the greater root of x² − 15x + 56 = 0.
8 Factorise into (x − 7)(x − 8) = 0. The roots are 7 and 8, so the greater root is 8.
12 questions · Seed 43 · Age guidance, not curriculum certification
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