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 − 17x + 30 = 0.
17 · 30 · 0 · Factored quadratic equations
2. Find the greater root of x² − 4x + 3 = 0.
4 · 3 · 0 · Factored quadratic equations
3. Find the greater root of x² − 20x + 96 = 0.
20 · 96 · 0 · Factored quadratic equations
4. Find the greater root of x² − 8x + 7 = 0.
8 · 7 · 0 · Factored quadratic equations
5. Find the greater root of x² − 11x + 30 = 0.
11 · 30 · 0 · Factored quadratic equations
6. Find the greater root of x² − 21x + 90 = 0.
21 · 90 · 0 · Factored quadratic equations
7. Find the greater root of x² − 15x + 26 = 0.
15 · 26 · 0 · Factored quadratic equations
8. Find the greater root of x² − 3x + 2 = 0.
3 · 2 · 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 − 11x + 10 = 0.
11 · 10 · 0 · Factored quadratic equations
11. Find the greater root of x² − 20x + 75 = 0.
20 · 75 · 0 · Factored quadratic equations
12. Find the greater root of x² − 12x + 35 = 0.
12 · 35 · 0 · Factored quadratic equations
12 questions · Seed 50 · 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 − 17x + 30 = 0.
15 Factorise into (x − 2)(x − 15) = 0. The roots are 2 and 15, so the greater root is 15.
2. 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.
3. 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.
4. 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.
5. 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.
6. Find the greater root of x² − 21x + 90 = 0.
15 Factorise into (x − 6)(x − 15) = 0. The roots are 6 and 15, so the greater root is 15.
7. Find the greater root of x² − 15x + 26 = 0.
13 Factorise into (x − 2)(x − 13) = 0. The roots are 2 and 13, so the greater root is 13.
8. 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.
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 − 11x + 10 = 0.
10 Factorise into (x − 1)(x − 10) = 0. The roots are 1 and 10, so the greater root is 10.
11. Find the greater root of x² − 20x + 75 = 0.
15 Factorise into (x − 5)(x − 15) = 0. The roots are 5 and 15, so the greater root is 15.
12. 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.
12 questions · Seed 50 · 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 − 17x + 30 = 0.
17 · 30 · 0 · Factored quadratic equations
2. Find the greater root of x² − 4x + 3 = 0.
4 · 3 · 0 · Factored quadratic equations
3. Find the greater root of x² − 20x + 96 = 0.
20 · 96 · 0 · Factored quadratic equations
4. Find the greater root of x² − 8x + 7 = 0.
8 · 7 · 0 · Factored quadratic equations
5. Find the greater root of x² − 11x + 30 = 0.
11 · 30 · 0 · Factored quadratic equations
6. Find the greater root of x² − 21x + 90 = 0.
21 · 90 · 0 · Factored quadratic equations
7. Find the greater root of x² − 15x + 26 = 0.
15 · 26 · 0 · Factored quadratic equations
8. Find the greater root of x² − 3x + 2 = 0.
3 · 2 · 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 − 11x + 10 = 0.
11 · 10 · 0 · Factored quadratic equations
11. Find the greater root of x² − 20x + 75 = 0.
20 · 75 · 0 · Factored quadratic equations
12. Find the greater root of x² − 12x + 35 = 0.
12 · 35 · 0 · Factored quadratic equations
12 questions · Seed 50 · 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 − 17x + 30 = 0.
15 Factorise into (x − 2)(x − 15) = 0. The roots are 2 and 15, so the greater root is 15.
2. 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.
3. 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.
4. 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.
5. 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.
6. Find the greater root of x² − 21x + 90 = 0.
15 Factorise into (x − 6)(x − 15) = 0. The roots are 6 and 15, so the greater root is 15.
7. Find the greater root of x² − 15x + 26 = 0.
13 Factorise into (x − 2)(x − 13) = 0. The roots are 2 and 13, so the greater root is 13.
8. 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.
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 − 11x + 10 = 0.
10 Factorise into (x − 1)(x − 10) = 0. The roots are 1 and 10, so the greater root is 10.
11. Find the greater root of x² − 20x + 75 = 0.
15 Factorise into (x − 5)(x − 15) = 0. The roots are 5 and 15, so the greater root is 15.
12. 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.
12 questions · Seed 50 · Age guidance, not curriculum certification
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