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=\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}


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