Discriminant Math Example 3

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

Example 3

easy
Find the discriminant of 2x2+5xโˆ’3=02x^2 + 5x - 3 = 0.

Solution

  1. 1
    ฮ”=52โˆ’4(2)(โˆ’3)=25+24=49\Delta = 5^2 - 4(2)(-3) = 25 + 24 = 49.
  2. 2
    ฮ”=49>0\Delta = 49 > 0: two distinct real solutions.

Answer

ฮ”=49\Delta = 49
A positive discriminant means two real solutions. Since 49 is a perfect square, the solutions are rational.

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 1 easy

Find the discriminant of [formula] and determine the number of solutions.

Example 2 medium

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

Example 4 medium

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

โ† All Discriminant Examples Discriminant Concept