Complex integers? Here a and b are integers. What are the possible values of a and b?

Complex integers? Here a and b are integers: What are the possible values of a and b? Notes and Solution Equating real and imaginary parts gives a2 + 2b2 = 9 and –ab = 2. Since a and b are integers the only possible values are a = 1 and b = -2 or a = -1 and b = 2.

Down under Solve

Down under Solve Notes and Solution

Quadratic shift x2 + 3x + c = 0 has complex roots x2 + 4x + c = 0 has distinct real roots c is an integer What is the value of c?

Quadratic shift x2 + 3x + c = 0 has complex roots ; x2 + 4x + c = 0 has distinct real roots; c is an integer. What is the value of c? Notes and Solution The discriminant of x2 + 3x + c is 9 – 4c. Since x2 + 3x + c = 0 has complex roots this is less than 0. i.e. 9 – 4c < 0 and so . The discriminant of x2 + 4x + c is 16 – 4c. Since x2 + 3x + c = 0 has distinct real roots this is greater than 0. i.e. 16 – 4c > 0 and so c < 4. Since c is an integer c must be 3.