The Quadratic Formula

Trinomials are not constantly basic to element. In fact, some trinomials cannot be factored. Thus, we need a different way to settle quadratic equations. Herein lies the prominence of the quadratic formula: Given a quadratic equation ax2 + bx + c = 0, the options are offered by the equation




You are watching: If the discriminant is 0 how many solutions are there

x =
*

Example 1: Solve for x: x2 + 8x + 15.75 = 0a = 1, b = 8, and c = 15.75.x = =

*
=
*
=
*
=
*
or
*
= - or- Thus, x = - or x = - .

Example 2: Solve for x: 3x2 - 10x - 25 = 0.a = 3, b = - 10, and also c = - 25.x = =

*
=
*
=
*
=
*
=
*
or
*
= 5 or- Thus, x = 5 or x = - .

Example 3: Solve for x: -3x2 - 24x - 48 = 0.a = - 3, b = - 24, and c = - 48.x = =

*
=
*
=
*
=
*
=
*
= - 4 Therefore, x = - 4.

Example 4: Solve for x: 2x2 - 4x + 7.a = 2, b = - 4, and also c = 7.x = =

*
=
*
=
*
Because we cannot take the square root of a negative number, tbelow are no options. (The graph of this quadratic polynomial will therefore be a parabola that never before touches the x-axis.)

The Discriminant

As we have viewed, tbelow have the right to be 0, 1, or 2 services to a quadratic equation, depending on whether the expression inside the square root authorize, (b2 - 4ac), is positive, negative, or zero. This expression has actually a distinct name: the discriminant.


Previous area Problems Next web page The Quadratic Formula web page 2

Take a Study Break


Sign up for our latest news and updates!
By entering your email address you agree to get emails from smashville247.net and also verify that you are over the age of 13. You deserve to view our Privacy Policy here. Unsubscribe from our emails at any type of time.
First Name
Last Name
Email
Sign Up

The #1 FREE study website for students

Many Popular More Aid


See more: How Far Is 10 Meters In Yards Conversion Calculator, Convert 10 Meters To Yards

Find Us On