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 − 20x + 96 = 0.
20 · 96 · 0 · Factored quadratic equations
2. Find the greater root of x² − 19x + 88 = 0.
19 · 88 · 0 · Factored quadratic equations
3. Find the greater root of x² − 12x + 11 = 0.
12 · 11 · 0 · Factored quadratic equations
4. Find the greater root of x² − 17x + 72 = 0.
17 · 72 · 0 · Factored quadratic equations
5. Find the greater root of x² − 9x + 20 = 0.
9 · 20 · 0 · Factored quadratic equations
6. Find the greater root of x² − 15x + 54 = 0.
15 · 54 · 0 · Factored quadratic equations
7. Find the greater root of x² − 3x + 2 = 0.
3 · 2 · 0 · Factored quadratic equations
8. Find the greater root of x² − 11x + 18 = 0.
11 · 18 · 0 · Factored quadratic equations
9. Find the greater root of x² − 18x + 77 = 0.
18 · 77 · 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 − 19x + 84 = 0.
19 · 84 · 0 · Factored quadratic equations
12. Find the greater root of x² − 13x + 30 = 0.
13 · 30 · 0 · Factored quadratic equations
12 questions · Seed 44 · 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 − 20x + 96 = 0.
12 Factorise into (x − 8)(x − 12) = 0. The roots are 8 and 12, so the greater root is 12.
2. Find the greater root of x² − 19x + 88 = 0.
11 Factorise into (x − 8)(x − 11) = 0. The roots are 8 and 11, so the greater root is 11.
3. 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.
4. Find the greater root of x² − 17x + 72 = 0.
9 Factorise into (x − 8)(x − 9) = 0. The roots are 8 and 9, so the greater root is 9.
5. 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.
6. Find the greater root of x² − 15x + 54 = 0.
9 Factorise into (x − 6)(x − 9) = 0. The roots are 6 and 9, so the greater root is 9.
7. Find the greater root of x² − 3x + 2 = 0.
2 Factorise into (x − 1)(x − 2) = 0. The roots are 1 and 2, so the greater root is 2.
8. 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.
9. Find the greater root of x² − 18x + 77 = 0.
11 Factorise into (x − 7)(x − 11) = 0. The roots are 7 and 11, so the greater root is 11.
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 − 19x + 84 = 0.
12 Factorise into (x − 7)(x − 12) = 0. The roots are 7 and 12, so the greater root is 12.
12. Find the greater root of x² − 13x + 30 = 0.
10 Factorise into (x − 3)(x − 10) = 0. The roots are 3 and 10, so the greater root is 10.
12 questions · Seed 44 · 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 − 20x + 96 = 0.
20 · 96 · 0 · Factored quadratic equations
2. Find the greater root of x² − 19x + 88 = 0.
19 · 88 · 0 · Factored quadratic equations
3. Find the greater root of x² − 12x + 11 = 0.
12 · 11 · 0 · Factored quadratic equations
4. Find the greater root of x² − 17x + 72 = 0.
17 · 72 · 0 · Factored quadratic equations
5. Find the greater root of x² − 9x + 20 = 0.
9 · 20 · 0 · Factored quadratic equations
6. Find the greater root of x² − 15x + 54 = 0.
15 · 54 · 0 · Factored quadratic equations
7. Find the greater root of x² − 3x + 2 = 0.
3 · 2 · 0 · Factored quadratic equations
8. Find the greater root of x² − 11x + 18 = 0.
11 · 18 · 0 · Factored quadratic equations
9. Find the greater root of x² − 18x + 77 = 0.
18 · 77 · 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 − 19x + 84 = 0.
19 · 84 · 0 · Factored quadratic equations
12. Find the greater root of x² − 13x + 30 = 0.
13 · 30 · 0 · Factored quadratic equations
12 questions · Seed 44 · 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 − 20x + 96 = 0.
12 Factorise into (x − 8)(x − 12) = 0. The roots are 8 and 12, so the greater root is 12.
2. Find the greater root of x² − 19x + 88 = 0.
11 Factorise into (x − 8)(x − 11) = 0. The roots are 8 and 11, so the greater root is 11.
3. 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.
4. Find the greater root of x² − 17x + 72 = 0.
9 Factorise into (x − 8)(x − 9) = 0. The roots are 8 and 9, so the greater root is 9.
5. 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.
6. Find the greater root of x² − 15x + 54 = 0.
9 Factorise into (x − 6)(x − 9) = 0. The roots are 6 and 9, so the greater root is 9.
7. Find the greater root of x² − 3x + 2 = 0.
2 Factorise into (x − 1)(x − 2) = 0. The roots are 1 and 2, so the greater root is 2.
8. 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.
9. Find the greater root of x² − 18x + 77 = 0.
11 Factorise into (x − 7)(x − 11) = 0. The roots are 7 and 11, so the greater root is 11.
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 − 19x + 84 = 0.
12 Factorise into (x − 7)(x − 12) = 0. The roots are 7 and 12, so the greater root is 12.
12. Find the greater root of x² − 13x + 30 = 0.
10 Factorise into (x − 3)(x − 10) = 0. The roots are 3 and 10, so the greater root is 10.
12 questions · Seed 44 · Age guidance, not curriculum certification
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