Use the discriminant to find unknown coefficients

Question 1

For which values of k does x² − 4x + k = 0 have no real roots?

• A. k = 4
• B. k < 4
• C. k > −4
• D. k > 4

Question 2

Work out the discriminant of x² − 6x − 8 = 0.

Answer 

Question 3

x² + 4x + k = 0 has exactly one (repeated) root. Find k.

Answer 

Question 4

For which values of k does x² + 6x + k = 0 have no real roots?

• A. k = 9
• B. k > 9
• C. k < 9
• D. k > −9

Question 5

Work out the discriminant of 5x² − 4x + 3 = 0.

Answer 

Question 6

x² + kx + 36 = 0 has equal roots and k is positive. Find k.

Answer 

Question 7

For which values of k does x² + 4x + k = 0 have two distinct real roots?

• A. k < 4
• B. k > −4
• C. k = 4
• D. k > 4

Question 8

Work out the discriminant of 4x² − 2x − 7 = 0.

Answer 

Question 9

x² + kx + 64 = 0 has equal roots and k is positive. Find k.

Answer 

Question 10

For which values of k does 2x² + 10x + k = 0 have no real roots?

• A. k > −12.5
• B. k < 12.5
• C. k > 12.5
• D. k = 12.5

Question 11

Work out the discriminant of 4x² − 8x − 8 = 0.

Answer 

Question 12

x² + kx + 9 = 0 has equal roots and k is positive. Find k.

Answer 

Question 13

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 14

Work out the discriminant of 3x² + 6x − 3 = 0.

Answer 

Question 15

x² + kx + 16 = 0 has equal roots and k is positive. Find k.

Answer 

Question 16

For which values of k does x² + 12x + k = 0 have no real roots?

• A. k < 36
• B. k > 36
• C. k = 36
• D. k > −36