Quadratic Formula MathBitsNotebook.com Terms of Use   Contact Person: Donna Roberts

The solutions for some quadratic equations are not rational, and cannot be obtained by factoring.
The
quadratic formula, however, may be used to solve ANY quadratic equation (even the ones that can be factored). This is a formula that you want to know and remember!

 • As you can see in the formula, the coefficients (numbers) "a", "b", and "c" from     ax2 + bx + c = 0 are substituted into the formula. • Also notice that the formula will yield two (±) solutions, since a quadratic is a     second degree equation. • The "2a" in the denominator is underneath the entire top, not just the radical. • Be careful with the "signs" of the "a", "b", and "c" values when substituting.

Let's see the Quadratic Formula at work in various situations:

 Solve: x2 + 2x - 15 = 0 Also factorable. Solution using Quadratic Formula: a = 1; b = 2; c = -15 This equation is also factorable. (x + 5)(x - 3) = 0 x = -5; x = 3 Notice that the quadratic formula ALSO gives the correct results. Notice the parentheses around the -15 to avoid confusion.

 Solve: 2x2 - 10x = -3 Not set equal to zero! Set equation equal to zero: 2x2 -10x + 3 = 0 Solution using Quadratic Formula: a = 2; b = -10; c = 3 Not factorable. Notice the needed parentheses for dealing with the "b" value of "-10". Radical answers are"exact" answers. Decimal answers are "approximate" answers most often used in applied word problems.

 Solve: x2 -10x + 25 = 0 Repeated answer! Solution using Quadratic Formula: a = 1; b = -10; c = 25 Be careful here! It appears that there is only ONE answer, but there is actually a "repeated" answer. This equation is also factorable. (x - 5)(x - 5) = 0 x = 5; x = 5 Answer repeats.

 Solve: x2 - 6x + 13 = 0 Negative under radical! Solution using Quadratic Formula: a = 1; b = -6; c = 13 Not factorable.

 NOTE: The re-posting of materials (in part or whole) from this site to the Internet is copyright violation and is not considered "fair use" for educators. Please read the "Terms of Use".