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 − 11x + 30 = 0.
11 · 30 · 0 · Factored quadratic equations
2. Find the greater root of x² − 8x + 7 = 0.
8 · 7 · 0 · Factored quadratic equations
3. Find the greater root of x² − 6x + 8 = 0.
6 · 8 · 0 · Factored quadratic equations
4. Find the greater root of x² − 12x + 32 = 0.
12 · 32 · 0 · Factored quadratic equations
5. Find the greater root of x² − 18x + 65 = 0.
18 · 65 · 0 · Factored quadratic equations
6. Find the greater root of x² − 9x + 8 = 0.
9 · 8 · 0 · Factored quadratic equations
7. Find the greater root of x² − 19x + 84 = 0.
19 · 84 · 0 · Factored quadratic equations
8. Find the greater root of x² − 16x + 60 = 0.
16 · 60 · 0 · Factored quadratic equations
9. Find the greater root of x² − 9x + 18 = 0.
9 · 18 · 0 · Factored quadratic equations
10. Find the greater root of x² − 14x + 33 = 0.
14 · 33 · 0 · Factored quadratic equations
11. Find the greater root of x² − 10x + 24 = 0.
10 · 24 · 0 · Factored quadratic equations
12. Find the greater root of x² − 7x + 10 = 0.
7 · 10 · 0 · Factored quadratic equations
12 questions · Seed 51 · 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 − 11x + 30 = 0.
6 Factorise into (x − 5)(x − 6) = 0. The roots are 5 and 6, so the greater root is 6.
2. Find the greater root of x² − 8x + 7 = 0.
7 Factorise into (x − 1)(x − 7) = 0. The roots are 1 and 7, so the greater root is 7.
3. 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.
4. Find the greater root of x² − 12x + 32 = 0.
8 Factorise into (x − 4)(x − 8) = 0. The roots are 4 and 8, so the greater root is 8.
5. 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.
6. Find the greater root of x² − 9x + 8 = 0.
8 Factorise into (x − 1)(x − 8) = 0. The roots are 1 and 8, so the greater root is 8.
7. 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.
8. 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.
9. Find the greater root of x² − 9x + 18 = 0.
6 Factorise into (x − 3)(x − 6) = 0. The roots are 3 and 6, so the greater root is 6.
10. 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.
11. Find the greater root of x² − 10x + 24 = 0.
6 Factorise into (x − 4)(x − 6) = 0. The roots are 4 and 6, so the greater root is 6.
12. Find the greater root of x² − 7x + 10 = 0.
5 Factorise into (x − 2)(x − 5) = 0. The roots are 2 and 5, so the greater root is 5.
12 questions · Seed 51 · 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 − 11x + 30 = 0.
11 · 30 · 0 · Factored quadratic equations
2. Find the greater root of x² − 8x + 7 = 0.
8 · 7 · 0 · Factored quadratic equations
3. Find the greater root of x² − 6x + 8 = 0.
6 · 8 · 0 · Factored quadratic equations
4. Find the greater root of x² − 12x + 32 = 0.
12 · 32 · 0 · Factored quadratic equations
5. Find the greater root of x² − 18x + 65 = 0.
18 · 65 · 0 · Factored quadratic equations
6. Find the greater root of x² − 9x + 8 = 0.
9 · 8 · 0 · Factored quadratic equations
7. Find the greater root of x² − 19x + 84 = 0.
19 · 84 · 0 · Factored quadratic equations
8. Find the greater root of x² − 16x + 60 = 0.
16 · 60 · 0 · Factored quadratic equations
9. Find the greater root of x² − 9x + 18 = 0.
9 · 18 · 0 · Factored quadratic equations
10. Find the greater root of x² − 14x + 33 = 0.
14 · 33 · 0 · Factored quadratic equations
11. Find the greater root of x² − 10x + 24 = 0.
10 · 24 · 0 · Factored quadratic equations
12. Find the greater root of x² − 7x + 10 = 0.
7 · 10 · 0 · Factored quadratic equations
12 questions · Seed 51 · 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 − 11x + 30 = 0.
6 Factorise into (x − 5)(x − 6) = 0. The roots are 5 and 6, so the greater root is 6.
2. Find the greater root of x² − 8x + 7 = 0.
7 Factorise into (x − 1)(x − 7) = 0. The roots are 1 and 7, so the greater root is 7.
3. 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.
4. Find the greater root of x² − 12x + 32 = 0.
8 Factorise into (x − 4)(x − 8) = 0. The roots are 4 and 8, so the greater root is 8.
5. 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.
6. Find the greater root of x² − 9x + 8 = 0.
8 Factorise into (x − 1)(x − 8) = 0. The roots are 1 and 8, so the greater root is 8.
7. 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.
8. 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.
9. Find the greater root of x² − 9x + 18 = 0.
6 Factorise into (x − 3)(x − 6) = 0. The roots are 3 and 6, so the greater root is 6.
10. 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.
11. Find the greater root of x² − 10x + 24 = 0.
6 Factorise into (x − 4)(x − 6) = 0. The roots are 4 and 6, so the greater root is 6.
12. Find the greater root of x² − 7x + 10 = 0.
5 Factorise into (x − 2)(x − 5) = 0. The roots are 2 and 5, so the greater root is 5.
12 questions · Seed 51 · Age guidance, not curriculum certification
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