Lesson What is the Discriminant in Quadratic equations?

Source code of 'What is the Discriminant in Quadratic equations?'

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About Quadratic1600: SQR -1 love Maths - I just do the odd maths question for fun in my spare time. My favourites vary from Probability to Quadratics and Completing the square but also equations

The discriminant is part of the quadratic formula (-b�sqr of b^2 - 4ac all divided by 2a)
If you work that through you will get solutions for x. However what about when you only want the number of roots. Well you can avoid using the quadratic formula by instead using the discriminant.

The discriminant is b^2 - 4ac - As you can see it is part of the quadratic formula. You may have noticed that when you are doing the quadratic formula if you get a minus number under the square root you can't get any further as you can't square root a minus number. You may have also come across the square root of 0 which will give only one solution. So as you can see that b^2 - 4ac is the part of the equation that decided how many roots there are going to be in the end result.

So by just using b^2 - 4ac we can save a lot of time

So here are some examples

x^2 + 4x + 4 = 0

(4)^2 - 4 x 4 x 1 = 0
16 -16 = 0 
We now know that this equation only has 1 solution

Take

x^2 + 5x - 4 = 0

(5)^2 - 4x-4x1 = 0
25 - -16 = 41
We now know what there are 2 solutions to that equation

Final example

x^2 + 2x + 20
(2)^2 - 4 x 1 x 20 = 0
4 - 80 = -76
We now know that there are 0 solutions

These examples hopefully show the value of using the discriminant