SOLVING QUADRAIC EQUATIONS WITH COMPLEX ROOTS WORKSHEET

Find exact values of a and b if 

Problem 1 :

3 + i is a root of x² + ax + b = 0, where a and b are real

Solution

Problem 2 :

1 - √2  is a root of x² + ax + b = 0, where a and b are rational

Solution

Problem 3 :

a + ai is a root of x² + 4x + b = 0, where a and b are real.

Solution

Problem 4 :

Find the exact values of a and b if √2 + i is a root of x² + ax + b = 0, where a and b are real numbers.

Solution

Problem 5 :

a+ai is a root of x² - 6x + b = 0, where a and b are real numbers. Find the values of a and b.

Solution

Problem 1 :

The roots of the equation x² – kx + k – 1 = 0 are α and 2α. Find the value(s) of k.

Solution

Problem 2 :

The roots of the quadratic equation

x² + 6x + c are k and k - 1

Find the value of c.

Solution

Problem 3 :

The roots of the quadratic equation

2x² - 9x + k

are m/2 and m - 3. Find the value of k.

Solution

Problem 4 :

Find the values of m for which one root of the equation

4x² + 5 = mx

is three times the other root.

Solution

Problem 5 :

One root of the equation 3x² - 4x + m = 0 is double the other. Find the roots, and the value of m.

Solution

Problem 6 :

The roots of the equation

4x² - kx + 35 = 0

differ by one. Find the value of k.

Solution