The Quadratic Formula

x= -b ± the square root of (b² – 4ac) all divided by 2a.

• "a" is the coefficient of x² 
• "b" is the coefficient of x 
• "c" is the constant

When you can't factor a quadratic equation, use a, b, and c to fill in the quadratic formula to solve. 

The expression inside the radical (the square root sign) is the discriminant. the discriminant could be used to find how many solutions a quadratic equation has.

• when the value of b² – 4ac is positive, there are two solutions

• when the value of b² – 4ac is 0, then there's one solution.
• when it is negative, then the equation has no solution

First, something easy. Find the amount of solutions for this:

x² - 2x - 15 = 0

For this problem, a=1, because the coefficient of x is 1. We also know b= -2, because the coefficient of x in the second part is -2. Lastly, c= -15. Let's fill these into b² - 4ac .

(-2)² - 4 (1) (-15)

So, (-2) multiplied by (-2) is 4, so:

4 - 4(1)(-15)

Now, let's solve the second term. 4 times 1 multiplied by -15 is -60, so:

You should be able to solve that.

64 is positive, so there are two solutions! Nice job~ ^__^

Okay, now let's try to solve one.

2x²-5x-3

-(-5)±√(-5)²-4(2)(-3)

2(2)

Okies, now let's solve a few parts...^__^

5±√25+24

4

Now, that's a lot smaller! Time to solve what's inside the radicand.

5±√49

4

Solve the square root of 49...

5±7

4

Now, as you can see it is 5 PLUS OR MINUS 7, so let's do both adding and subtracting here:

                                                                                                            x=      5+7                                                        x=      5-7

                                                                                                                         4                                                                     4

                                                                                                             12                                                                                             -2

                                                                                                              4                                                                                               4

                                                                                                                    3                                                                              -½

  <---That's me! Here's an EXAMPLE of a problem done. So sorry it's messy. To all you people who use your scanners, I think this thing only uploads JPEG files. Try that if you have trouble uploading.

**Second example is from: http://www.coolmath.com/algebra/Algebra1/11Quadratics/05_quadranator.htm

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