Back to worksheets Maths Ages 16-18
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 16-18
Factored quadratic equations Take your time. Show your thinking.
1. Find the greater root of x² − 17x + 70 = 0.
17 · 70 · 0 · Factored quadratic equations
2. Find the greater root of x² − 17x + 30 = 0.
17 · 30 · 0 · Factored quadratic equations
3. Find the greater root of x² − 15x + 50 = 0.
15 · 50 · 0 · Factored quadratic equations
4. Find the greater root of x² − 20x + 75 = 0.
20 · 75 · 0 · Factored quadratic equations
5. Find the greater root of x² − 11x + 24 = 0.
11 · 24 · 0 · Factored quadratic equations
6. Find the greater root of x² − 16x + 63 = 0.
16 · 63 · 0 · Factored quadratic equations
7. Find the greater root of x² − 12x + 11 = 0.
12 · 11 · 0 · Factored quadratic equations
8. Find the greater root of x² − 13x + 42 = 0.
13 · 42 · 0 · Factored quadratic equations
9. Find the greater root of x² − 6x + 8 = 0.
6 · 8 · 0 · Factored quadratic equations
10. Find the greater root of x² − 7x + 12 = 0.
7 · 12 · 0 · Factored quadratic equations
11. Find the greater root of x² − 20x + 96 = 0.
20 · 96 · 0 · Factored quadratic equations
12. Find the greater root of x² − 23x + 120 = 0.
23 · 120 · 0 · Factored quadratic equations
12 questions · Seed 52 · Age guidance, not curriculum certification
View the answer key Worksheet Studio Answer key · Ages 16-18
Factored quadratic equations Answers and reasoning. Review before teaching.
1. 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.
2. Find the greater root of x² − 17x + 30 = 0.
15 Factorise into (x − 2)(x − 15) = 0. The roots are 2 and 15, so the greater root is 15.
3. 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.
4. Find the greater root of x² − 20x + 75 = 0.
15 Factorise into (x − 5)(x − 15) = 0. The roots are 5 and 15, so the greater root is 15.
5. 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.
6. 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.
7. Find the greater root of x² − 12x + 11 = 0.
11 Factorise into (x − 1)(x − 11) = 0. The roots are 1 and 11, so the greater root is 11.
8. Find the greater root of x² − 13x + 42 = 0.
7 Factorise into (x − 6)(x − 7) = 0. The roots are 6 and 7, so the greater root is 7.
9. Find the greater root of x² − 6x + 8 = 0.
4 Factorise into (x − 2)(x − 4) = 0. The roots are 2 and 4, so the greater root is 4.
10. 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.
11. 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.
12. Find the greater root of x² − 23x + 120 = 0.
15 Factorise into (x − 8)(x − 15) = 0. The roots are 8 and 15, so the greater root is 15.
12 questions · Seed 52 · Age guidance, not curriculum certification
Worksheet Studio Practice pack · Ages 16-18
Factored quadratic equations Take your time. Show your thinking.
1. Find the greater root of x² − 17x + 70 = 0.
17 · 70 · 0 · Factored quadratic equations
2. Find the greater root of x² − 17x + 30 = 0.
17 · 30 · 0 · Factored quadratic equations
3. Find the greater root of x² − 15x + 50 = 0.
15 · 50 · 0 · Factored quadratic equations
4. Find the greater root of x² − 20x + 75 = 0.
20 · 75 · 0 · Factored quadratic equations
5. Find the greater root of x² − 11x + 24 = 0.
11 · 24 · 0 · Factored quadratic equations
6. Find the greater root of x² − 16x + 63 = 0.
16 · 63 · 0 · Factored quadratic equations
7. Find the greater root of x² − 12x + 11 = 0.
12 · 11 · 0 · Factored quadratic equations
8. Find the greater root of x² − 13x + 42 = 0.
13 · 42 · 0 · Factored quadratic equations
9. Find the greater root of x² − 6x + 8 = 0.
6 · 8 · 0 · Factored quadratic equations
10. Find the greater root of x² − 7x + 12 = 0.
7 · 12 · 0 · Factored quadratic equations
11. Find the greater root of x² − 20x + 96 = 0.
20 · 96 · 0 · Factored quadratic equations
12. Find the greater root of x² − 23x + 120 = 0.
23 · 120 · 0 · Factored quadratic equations
12 questions · Seed 52 · Age guidance, not curriculum certification
Worksheet Studio Answer key · Ages 16-18
Factored quadratic equations Answers and reasoning. Review before teaching.
1. 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.
2. Find the greater root of x² − 17x + 30 = 0.
15 Factorise into (x − 2)(x − 15) = 0. The roots are 2 and 15, so the greater root is 15.
3. 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.
4. Find the greater root of x² − 20x + 75 = 0.
15 Factorise into (x − 5)(x − 15) = 0. The roots are 5 and 15, so the greater root is 15.
5. 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.
6. 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.
7. Find the greater root of x² − 12x + 11 = 0.
11 Factorise into (x − 1)(x − 11) = 0. The roots are 1 and 11, so the greater root is 11.
8. Find the greater root of x² − 13x + 42 = 0.
7 Factorise into (x − 6)(x − 7) = 0. The roots are 6 and 7, so the greater root is 7.
9. Find the greater root of x² − 6x + 8 = 0.
4 Factorise into (x − 2)(x − 4) = 0. The roots are 2 and 4, so the greater root is 4.
10. 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.
11. 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.
12. Find the greater root of x² − 23x + 120 = 0.
15 Factorise into (x − 8)(x − 15) = 0. The roots are 8 and 15, so the greater root is 15.
12 questions · Seed 52 · Age guidance, not curriculum certification
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