## week 7 precalc 11

This week in Precalc 11 we finished unit 3 with the quadratic equation and interpreting the discriminant.

In lesson 3.4 we learned how to use the quadratic formula : $x=-b \mp \frac{\sqrt{b^2-4ac}}{2a}$ to solve quadratic equations.  i found this especially useful with fractions and decimals.

Ex :

$x=2x^2-6x+1=0$

$x=\frac{6 \mp \sqrt{6^2-4(2)(1)}}{4}$

$x=\frac{6 \mp \sqrt {28}}{4}$

$x=\frac{3 \mp \sqrt{7}}{2}$

In lesson 3.5 we learned how to interpret the discriminant : $b^2-4ac$ and how to find whether they are equal roots, real roots, no real roots etc.  We also learned how to find the value of a variable when the equation has no real roots, one real root etc.

$b^2-4ac \textgreater 0 = 2$ solutions/real root

$b^2-4ac = 1$ solution/equal root

$b^2-4ac \textless 0 = 0$ solutions/no real roots

Ex :  $8x^2-5x+k=0$

determine the value of K when the equation has no real roots:

$5^2-4(8)k \textless k$

$25 - 32k \textless 0$

$\frac{25}{32} \textless 32k$

$k \textgreater \frac{25}{32}$