This week in Pre-Calc we learned about discriminants. A discriminant gives information about the roots of the quadratic equation. We use to find the value.

• If it is less than 0, there are no real roots.
• If it is equal to 0, there’s one real root.
• If it is greater than, 0 there are two real roots.

Ex:

a=2, b=-7 c=3

step 1:

step 2:

step 3:

The discriminant is 25, because it is greater than 0, this means that this quadratic equation has two real roots.

This week in pre-calc we’ve been learning how to use factoring to solve quadratic equations. Something I challenged with at first was using the perfect square trinomial method because of all the steps involved.

Example:

There are no two numbers that add to -8 and 9 so the first thing to do is move the 9 to the other side. Now we can find a something in common to take out of the

1. before factoring the trinomial I factored out the 2.
2. I moved the 9 back over and the +4 -4 are now                                                           there because we took the half of 4 which is two                                                            and the squared it to put it back in.
3. the -8 is now there because the 2 in front of the brackets                                                      needs to be mulitiplied with the -4 in order to take                                                       it out of the brackets.
4. in this part the -8 is subtracted by the 9 and which gave us +1                                         and we moved it over to the right side of the equation.
5. = divide both sides by 2 to get rid of the                                                                                coefficient in front of the brackets.
6. to get rid of the x-2 squared both sides need to                                                                be square rooted.
7. At this point we can see there’s a negative under the root which is not possible because we can’t square root a negative number. This means that this equation has no solution.