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 − 15x + 56 = 0.
15 · 56 · 0 · Factored quadratic equations
2. Find the greater root of x² − 19x + 84 = 0.
19 · 84 · 0 · Factored quadratic equations
3. Find the greater root of x² − 14x + 33 = 0.
14 · 33 · 0 · Factored quadratic equations
4. Find the greater root of x² − 10x + 21 = 0.
10 · 21 · 0 · Factored quadratic equations
5. Find the greater root of x² − 22x + 105 = 0.
22 · 105 · 0 · Factored quadratic equations
6. Find the greater root of x² − 18x + 56 = 0.
18 · 56 · 0 · Factored quadratic equations
7. Find the greater root of x² − 18x + 80 = 0.
18 · 80 · 0 · Factored quadratic equations
8. Find the greater root of x² − 11x + 30 = 0.
11 · 30 · 0 · Factored quadratic equations
9. Find the greater root of x² − 19x + 70 = 0.
19 · 70 · 0 · Factored quadratic equations
10. Find the greater root of x² − 21x + 98 = 0.
21 · 98 · 0 · Factored quadratic equations
11. Find the greater root of x² − 10x + 9 = 0.
10 · 9 · 0 · Factored quadratic equations
12. Find the greater root of x² − 4x + 3 = 0.
4 · 3 · 0 · Factored quadratic equations
12 questions · Seed 45 · 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 − 15x + 56 = 0.
8 Factorise into (x − 7)(x − 8) = 0. The roots are 7 and 8, so the greater root is 8.
2. Find the greater root of x² − 19x + 84 = 0.
12 Factorise into (x − 7)(x − 12) = 0. The roots are 7 and 12, so the greater root is 12.
3. Find the greater root of x² − 14x + 33 = 0.
11 Factorise into (x − 3)(x − 11) = 0. The roots are 3 and 11, so the greater root is 11.
4. Find the greater root of x² − 10x + 21 = 0.
7 Factorise into (x − 3)(x − 7) = 0. The roots are 3 and 7, so the greater root is 7.
5. Find the greater root of x² − 22x + 105 = 0.
15 Factorise into (x − 7)(x − 15) = 0. The roots are 7 and 15, so the greater root is 15.
6. Find the greater root of x² − 18x + 56 = 0.
14 Factorise into (x − 4)(x − 14) = 0. The roots are 4 and 14, so the greater root is 14.
7. Find the greater root of x² − 18x + 80 = 0.
10 Factorise into (x − 8)(x − 10) = 0. The roots are 8 and 10, so the greater root is 10.
8. 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.
9. 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.
10. Find the greater root of x² − 21x + 98 = 0.
14 Factorise into (x − 7)(x − 14) = 0. The roots are 7 and 14, so the greater root is 14.
11. 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.
12. Find the greater root of x² − 4x + 3 = 0.
3 Factorise into (x − 1)(x − 3) = 0. The roots are 1 and 3, so the greater root is 3.
12 questions · Seed 45 · 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 − 15x + 56 = 0.
15 · 56 · 0 · Factored quadratic equations
2. Find the greater root of x² − 19x + 84 = 0.
19 · 84 · 0 · Factored quadratic equations
3. Find the greater root of x² − 14x + 33 = 0.
14 · 33 · 0 · Factored quadratic equations
4. Find the greater root of x² − 10x + 21 = 0.
10 · 21 · 0 · Factored quadratic equations
5. Find the greater root of x² − 22x + 105 = 0.
22 · 105 · 0 · Factored quadratic equations
6. Find the greater root of x² − 18x + 56 = 0.
18 · 56 · 0 · Factored quadratic equations
7. Find the greater root of x² − 18x + 80 = 0.
18 · 80 · 0 · Factored quadratic equations
8. Find the greater root of x² − 11x + 30 = 0.
11 · 30 · 0 · Factored quadratic equations
9. Find the greater root of x² − 19x + 70 = 0.
19 · 70 · 0 · Factored quadratic equations
10. Find the greater root of x² − 21x + 98 = 0.
21 · 98 · 0 · Factored quadratic equations
11. Find the greater root of x² − 10x + 9 = 0.
10 · 9 · 0 · Factored quadratic equations
12. Find the greater root of x² − 4x + 3 = 0.
4 · 3 · 0 · Factored quadratic equations
12 questions · Seed 45 · 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 − 15x + 56 = 0.
8 Factorise into (x − 7)(x − 8) = 0. The roots are 7 and 8, so the greater root is 8.
2. Find the greater root of x² − 19x + 84 = 0.
12 Factorise into (x − 7)(x − 12) = 0. The roots are 7 and 12, so the greater root is 12.
3. Find the greater root of x² − 14x + 33 = 0.
11 Factorise into (x − 3)(x − 11) = 0. The roots are 3 and 11, so the greater root is 11.
4. Find the greater root of x² − 10x + 21 = 0.
7 Factorise into (x − 3)(x − 7) = 0. The roots are 3 and 7, so the greater root is 7.
5. Find the greater root of x² − 22x + 105 = 0.
15 Factorise into (x − 7)(x − 15) = 0. The roots are 7 and 15, so the greater root is 15.
6. Find the greater root of x² − 18x + 56 = 0.
14 Factorise into (x − 4)(x − 14) = 0. The roots are 4 and 14, so the greater root is 14.
7. Find the greater root of x² − 18x + 80 = 0.
10 Factorise into (x − 8)(x − 10) = 0. The roots are 8 and 10, so the greater root is 10.
8. 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.
9. 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.
10. Find the greater root of x² − 21x + 98 = 0.
14 Factorise into (x − 7)(x − 14) = 0. The roots are 7 and 14, so the greater root is 14.
11. 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.
12. Find the greater root of x² − 4x + 3 = 0.
3 Factorise into (x − 1)(x − 3) = 0. The roots are 1 and 3, so the greater root is 3.
12 questions · Seed 45 · Age guidance, not curriculum certification
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