High School Mathematics 6.5 Forming a Quadratic Equation Using Its Roots

Let a and b be the roots of the quadratic equation, then the required equation is
x^{2} - (a + b)x + (a*b) = 0.

Example:
Find the quadratic equation whose roots are 5 and 3. Solution:
Given that, roots of the equation are 5 and 3
Therefore, the required quadratic equation is
x^{2} - (a + b)x + (a*b) = 0.
Substituting the value of roots in the above equation we get the required equation.
x^{2} - (5+3)x + 5*3 = 0
x^{2} - 8x + 15 = 0.

Directions: Solve the following problems. Also write at least 5 examples of your own.