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 − 16x + 60 = 0.
16 · 60 · 0 · Factored quadratic equations
2. Find the greater root of x² − 19x + 60 = 0.
19 · 60 · 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 − 14x + 24 = 0.
14 · 24 · 0 · Factored quadratic equations
5. Find the greater root of x² − 10x + 9 = 0.
10 · 9 · 0 · Factored quadratic equations
6. Find the greater root of x² − 11x + 18 = 0.
11 · 18 · 0 · Factored quadratic equations
7. Find the greater root of x² − 19x + 70 = 0.
19 · 70 · 0 · Factored quadratic equations
8. Find the greater root of x² − 22x + 112 = 0.
22 · 112 · 0 · Factored quadratic equations
9. Find the greater root of x² − 18x + 45 = 0.
18 · 45 · 0 · Factored quadratic equations
10. Find the greater root of x² − 17x + 66 = 0.
17 · 66 · 0 · Factored quadratic equations
11. Find the greater root of x² − 14x + 13 = 0.
14 · 13 · 0 · Factored quadratic equations
12. Find the greater root of x² − 13x + 12 = 0.
13 · 12 · 0 · Factored quadratic equations
12 questions · Seed 104729 · 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 − 16x + 60 = 0.
10 Factorise into (x − 6)(x − 10) = 0. The roots are 6 and 10, so the greater root is 10.
2. Find the greater root of x² − 19x + 60 = 0.
15 Factorise into (x − 4)(x − 15) = 0. The roots are 4 and 15, so the greater root is 15.
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 − 14x + 24 = 0.
12 Factorise into (x − 2)(x − 12) = 0. The roots are 2 and 12, so the greater root is 12.
5. Find the greater root of x² − 10x + 9 = 0.
9 Factorise into (x − 1)(x − 9) = 0. The roots are 1 and 9, so the greater root is 9.
6. 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.
7. Find the greater root of x² − 19x + 70 = 0.
14 Factorise into (x − 5)(x − 14) = 0. The roots are 5 and 14, so the greater root is 14.
8. 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.
9. 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.
10. 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.
11. 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. Find the greater root of x² − 13x + 12 = 0.
12 Factorise into (x − 1)(x − 12) = 0. The roots are 1 and 12, so the greater root is 12.
12 questions · Seed 104729 · 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 − 16x + 60 = 0.
16 · 60 · 0 · Factored quadratic equations
2. Find the greater root of x² − 19x + 60 = 0.
19 · 60 · 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 − 14x + 24 = 0.
14 · 24 · 0 · Factored quadratic equations
5. Find the greater root of x² − 10x + 9 = 0.
10 · 9 · 0 · Factored quadratic equations
6. Find the greater root of x² − 11x + 18 = 0.
11 · 18 · 0 · Factored quadratic equations
7. Find the greater root of x² − 19x + 70 = 0.
19 · 70 · 0 · Factored quadratic equations
8. Find the greater root of x² − 22x + 112 = 0.
22 · 112 · 0 · Factored quadratic equations
9. Find the greater root of x² − 18x + 45 = 0.
18 · 45 · 0 · Factored quadratic equations
10. Find the greater root of x² − 17x + 66 = 0.
17 · 66 · 0 · Factored quadratic equations
11. Find the greater root of x² − 14x + 13 = 0.
14 · 13 · 0 · Factored quadratic equations
12. Find the greater root of x² − 13x + 12 = 0.
13 · 12 · 0 · Factored quadratic equations
12 questions · Seed 104729 · 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 − 16x + 60 = 0.
10 Factorise into (x − 6)(x − 10) = 0. The roots are 6 and 10, so the greater root is 10.
2. Find the greater root of x² − 19x + 60 = 0.
15 Factorise into (x − 4)(x − 15) = 0. The roots are 4 and 15, so the greater root is 15.
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 − 14x + 24 = 0.
12 Factorise into (x − 2)(x − 12) = 0. The roots are 2 and 12, so the greater root is 12.
5. Find the greater root of x² − 10x + 9 = 0.
9 Factorise into (x − 1)(x − 9) = 0. The roots are 1 and 9, so the greater root is 9.
6. 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.
7. Find the greater root of x² − 19x + 70 = 0.
14 Factorise into (x − 5)(x − 14) = 0. The roots are 5 and 14, so the greater root is 14.
8. 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.
9. 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.
10. 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.
11. 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. Find the greater root of x² − 13x + 12 = 0.
12 Factorise into (x − 1)(x − 12) = 0. The roots are 1 and 12, so the greater root is 12.
12 questions · Seed 104729 · Age guidance, not curriculum certification
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