Discriminant Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Find the discriminant of x2โˆ’6x+9=0x^2 - 6x + 9 = 0 and determine the number of solutions.

Solution

  1. 1
    Identify a=1,b=โˆ’6,c=9a = 1, b = -6, c = 9.
  2. 2
    Discriminant: ฮ”=b2โˆ’4ac=36โˆ’36=0\Delta = b^2 - 4ac = 36 - 36 = 0.
  3. 3
    Since ฮ”=0\Delta = 0, there is exactly one real solution (a repeated root).

Answer

ฮ”=0\Delta = 0; one repeated solution (x=3x = 3).
The discriminant ฮ”=b2โˆ’4ac\Delta = b^2 - 4ac tells us the nature of the roots: ฮ”>0\Delta > 0 means two distinct real roots, ฮ”=0\Delta = 0 means one repeated root, ฮ”<0\Delta < 0 means no real roots.

About Discriminant

The discriminant of a quadratic equation ax2+bx+c=0ax^2 + bx + c = 0 is the expression ฮ”=b2โˆ’4ac\Delta = b^2 - 4ac. It determines the number and nature of the solutions.

Learn more about Discriminant โ†’

More Discriminant Examples

Example 2 medium

For what values of [formula] does [formula] have two distinct real solutions?

Example 3 easy

Find the discriminant of [formula].

Example 4 medium

Without solving, how many real solutions does [formula] have?

โ† All Discriminant Examples Discriminant Concept