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 − 7x + 6 = 0.
7 · 6 · 0 · Factored quadratic equations
2. Find the greater root of x² − 17x + 70 = 0.
17 · 70 · 0 · Factored quadratic equations
3. Find the greater root of x² − 18x + 72 = 0.
18 · 72 · 0 · Factored quadratic equations
4. Find the greater root of x² − 12x + 35 = 0.
12 · 35 · 0 · Factored quadratic equations
5. Find the greater root of x² − 15x + 36 = 0.
15 · 36 · 0 · Factored quadratic equations
6. Find the greater root of x² − 16x + 60 = 0.
16 · 60 · 0 · Factored quadratic equations
7. Find the greater root of x² − 19x + 78 = 0.
19 · 78 · 0 · Factored quadratic equations
8. Find the greater root of x² − 17x + 66 = 0.
17 · 66 · 0 · Factored quadratic equations
9. Find the greater root of x² − 13x + 40 = 0.
13 · 40 · 0 · Factored quadratic equations
10. Find the greater root of x² − 12x + 27 = 0.
12 · 27 · 0 · Factored quadratic equations
11. Find the greater root of x² − 15x + 50 = 0.
15 · 50 · 0 · Factored quadratic equations
12. Find the greater root of x² − 8x + 12 = 0.
8 · 12 · 0 · Factored quadratic equations
12 questions · Seed 59 · 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 − 7x + 6 = 0.
6 Factorise into (x − 1)(x − 6) = 0. The roots are 1 and 6, so the greater root is 6.
2. 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.
3. 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.
4. 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.
5. 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.
6. Find the greater root of x² − 16x + 60 = 0.
10 Factorise into (x − 6)(x − 10) = 0. The roots are 6 and 10, so the greater root is 10.
7. Find the greater root of x² − 19x + 78 = 0.
13 Factorise into (x − 6)(x − 13) = 0. The roots are 6 and 13, so the greater root is 13.
8. Find the greater root of x² − 17x + 66 = 0.
11 Factorise into (x − 6)(x − 11) = 0. The roots are 6 and 11, so the greater root is 11.
9. Find the greater root of x² − 13x + 40 = 0.
8 Factorise into (x − 5)(x − 8) = 0. The roots are 5 and 8, so the greater root is 8.
10. Find the greater root of x² − 12x + 27 = 0.
9 Factorise into (x − 3)(x − 9) = 0. The roots are 3 and 9, so the greater root is 9.
11. 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.
12. Find the greater root of x² − 8x + 12 = 0.
6 Factorise into (x − 2)(x − 6) = 0. The roots are 2 and 6, so the greater root is 6.
12 questions · Seed 59 · 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 − 7x + 6 = 0.
7 · 6 · 0 · Factored quadratic equations
2. Find the greater root of x² − 17x + 70 = 0.
17 · 70 · 0 · Factored quadratic equations
3. Find the greater root of x² − 18x + 72 = 0.
18 · 72 · 0 · Factored quadratic equations
4. Find the greater root of x² − 12x + 35 = 0.
12 · 35 · 0 · Factored quadratic equations
5. Find the greater root of x² − 15x + 36 = 0.
15 · 36 · 0 · Factored quadratic equations
6. Find the greater root of x² − 16x + 60 = 0.
16 · 60 · 0 · Factored quadratic equations
7. Find the greater root of x² − 19x + 78 = 0.
19 · 78 · 0 · Factored quadratic equations
8. Find the greater root of x² − 17x + 66 = 0.
17 · 66 · 0 · Factored quadratic equations
9. Find the greater root of x² − 13x + 40 = 0.
13 · 40 · 0 · Factored quadratic equations
10. Find the greater root of x² − 12x + 27 = 0.
12 · 27 · 0 · Factored quadratic equations
11. Find the greater root of x² − 15x + 50 = 0.
15 · 50 · 0 · Factored quadratic equations
12. Find the greater root of x² − 8x + 12 = 0.
8 · 12 · 0 · Factored quadratic equations
12 questions · Seed 59 · 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 − 7x + 6 = 0.
6 Factorise into (x − 1)(x − 6) = 0. The roots are 1 and 6, so the greater root is 6.
2. 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.
3. 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.
4. 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.
5. 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.
6. Find the greater root of x² − 16x + 60 = 0.
10 Factorise into (x − 6)(x − 10) = 0. The roots are 6 and 10, so the greater root is 10.
7. Find the greater root of x² − 19x + 78 = 0.
13 Factorise into (x − 6)(x − 13) = 0. The roots are 6 and 13, so the greater root is 13.
8. Find the greater root of x² − 17x + 66 = 0.
11 Factorise into (x − 6)(x − 11) = 0. The roots are 6 and 11, so the greater root is 11.
9. Find the greater root of x² − 13x + 40 = 0.
8 Factorise into (x − 5)(x − 8) = 0. The roots are 5 and 8, so the greater root is 8.
10. Find the greater root of x² − 12x + 27 = 0.
9 Factorise into (x − 3)(x − 9) = 0. The roots are 3 and 9, so the greater root is 9.
11. 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.
12. Find the greater root of x² − 8x + 12 = 0.
6 Factorise into (x − 2)(x − 6) = 0. The roots are 2 and 6, so the greater root is 6.
12 questions · Seed 59 · Age guidance, not curriculum certification
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