Use the discriminant to find unknown coefficients
10th grade (Year 11 in England) · 16 questions · Common Core: HSA.REI.B.4.B · England: GCSE Higher Algebra, A-level Pure Mathematics
Name
Date
Score/ 16
Question 1
x² + 4x + k = 0 has exactly one (repeated) root. Find k.
Answer
Question 2
Work out the discriminant of 5x² − 2x − 8 = 0.
Answer
Question 3
For which values of k does x² − 6x + k = 0 have two distinct real roots?
- A. k = 9
- B. k > −9
- C. k > 9
- D. k < 9
Question 4
x² + 12x + k = 0 has exactly one (repeated) root. Find k.
Answer
Question 5
Work out the discriminant of x² + 7x + 1 = 0.
Answer
Question 6
For which values of k does 2x² + 8x + k = 0 have no real roots?
- A. k > −8
- B. k > 8
- C. k < 8
- D. k = 8
Question 7
x² + kx + 49 = 0 has equal roots and k is positive. Find k.
Answer
Question 8
Work out the discriminant of x² − 9x − 9 = 0.
Answer
Question 9
For which values of k does x² + 12x + k = 0 have two distinct real roots?
- A. k < 36
- B. k > 36
- C. k = 36
- D. k > −36
Question 10
x² + kx + 49 = 0 has equal roots and k is positive. Find k.
Answer
Question 11
Work out the discriminant of 4x² + 8x + 9 = 0.
Answer
Question 12
For which values of k does x² − 8x + k = 0 have two distinct real roots?
- A. k = 16
- B. k > −16
- C. k < 16
- D. k > 16
Question 13
x² + kx + 64 = 0 has equal roots and k is positive. Find k.
Answer
Question 14
Work out the discriminant of 5x² − 8x − 8 = 0.
Answer
Question 15
For which values of k does x² − 12x + k = 0 have two distinct real roots?
- A. k > 36
- B. k = 36
- C. k < 36
- D. k > −36
Question 16
x² − 14x + k = 0 has exactly one (repeated) root. Find k.
Answer
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