## Week 7 – Interpreting the Discriminant

This week I learned how to interpret the discriminant.

Here is a common question:

This question asked me to determine the values of k for which each equation has no real roots. The first thing you need to do is determine a formula for the discriminant which is the part of the equation in the quadratic formula under the radicand $b^{2}-4ac<0$. You make the formula to less than zero because you want the discriminant to be negative, you can’t take a root of a negative number so the equation will have no real roots. Then you substitute a b and c into to the and use BEDMAS to solve for k. You figure out if k is less than $\frac{-27}{4}$ there will be no answer to the equation because the discriminant is negative.

## Week 6 – Using Square Roots to Solve Quadratic Equations

This week I learned how to solve quadratic equations using square roots.

Here is a common question:

This question asked me to solve the equation by completing the square. The first thing you need to do in this question is make it a square. You figure out the square by chopping the middle term in half $\frac{5}{2}$ then square it $\frac{25}{4}$. You add $\frac{25}{4}$ into the equation by making it a zero pair. Then you can solve for x by simplifying the part of the equation that is in brackets to $(x+5/2)^{2}$ and add together the part not in brackets to get $\frac{-37}{4}$. After you have done this you move $\frac{37}{4}$ to the other side of the equation and square root the whole thing. Then you can move $\frac{5}{2}$ to the other side. Once you have done this you have simplified for x.