Discriminant Math Example 4

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

Example 4

medium
Without solving, how many real solutions does 3x2+2x+5=03x^2 + 2x + 5 = 0 have?

Solution

  1. 1
    ฮ”=4โˆ’4(3)(5)=4โˆ’60=โˆ’56\Delta = 4 - 4(3)(5) = 4 - 60 = -56.
  2. 2
    ฮ”<0\Delta < 0: no real solutions.

Answer

No real solutions.
The discriminant is negative, so the parabola does not cross the xx-axis. All solutions are complex.

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 3 easy

Find the discriminant of [formula].

โ† All Discriminant Examples Discriminant Concept