FINDING UNKNOWN INVOLVING SUM AND PRODUCT OF ROOTS WORKSHEET

Use the sum and product of roots formulas to answer the questions below :

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

Solution

2)  The roots of the quadratic equation

x² + 6x + c are k and k - 1

Find the value of c.

Solution

3)  The roots of the quadratic equation

2x² - 9x + k

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

Solution

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

4x² + 5 = mx

is three times the other root.

Solution

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

Solution

6)  The roots of the equation

4x² - kx + 35 = 0

differ by one. Find the value of k.

Solution

Problem 1 :

Find k if the difference between the roots of the quadratic equation

x² – 4x + k = 0 is 2

Solution

Problem 2 :

Find the value of p such that the difference of the roots of the equation

x² – px + 8 = 0 is 2

Solution

Problem 3 :

Find the value of k such that the difference of the roots of the equation

2kx² – 20x + 21 = 0 is 2

Solution

Problem 4 :

Find k so that one root of the equation 2x² – 16x + k = 0 is twice the other. (Hint : One root = α, Other root = 2α)

Solution

Problem 5 :

Find k so that one root of the equation

k(x – 1)² = 5x – 7

is twice the other.                 Solution

Problem 6 :

Find k so that the roots of the quadratic equation

2x² + 3x + k = 0

are equal.                        Solution

Problem 7 :

If 1 – i and 1 + i are the roots of the equation

x² + ax + b = 0

where a, b ∈  r, then find the values of a and b.

Solution