Unit 4, Lesson 16
Solving Quadratics (Optional)
Algebra 2
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What number should be added to the expression \(x^2 - 15x\) to result in an expression equivalent to a perfect square?
-7.5
7.5
-56.25
56.25
Noah uses the quadratic formula to solve the equation \(2x^2+3x-5=4\). He finds \(x = \text-2.5\) or 1. But, when he checks his answer, he finds that neither -2.5 nor 1 are solutions to the equation. Here are his steps:
\(a=2\), \(b=3\), \(c=\text-5\)
\(x=\frac{\text-3 \pm \sqrt{3^2 - 4 \boldcdot 2 \boldcdot \text-5}}{2 \boldcdot 2}\)
\(x=\frac{\text-3 \pm \sqrt{49}}{4}\)
\(x = \text-2.5\) or 1
Solve each quadratic equation with the method of your choice.
What are the solutions to the equation \(x^2-4x=\text-3\)?
\(\frac{4 \pm \sqrt{16 - 4 \boldcdot 0 \boldcdot \text-3}}{2 \boldcdot 0}\)
\(\frac{4 \pm \sqrt{16 - 4 \boldcdot 1 \boldcdot \text-3}}{2 \boldcdot 1}\)
\(\frac{4 \pm \sqrt{16 - 4 \boldcdot 1 \boldcdot 3}}{2 \boldcdot 1}\)
\(\frac{\text-4 \pm \sqrt{16 - 4 \boldcdot 1 \boldcdot 3}}{2 \boldcdot 1}\)
Which expression is equivalent to \(\sqrt{\text-23}\)?
\(\text-23i\)
\(23i\)
\(\text- i \sqrt{23}\)
\(i \sqrt{23}\)
Write each expression in the form \(a+bi\), where \(a\) and \(b\) are real numbers.
\(5i^2\)
\(i^2 \boldcdot i^2\)
\((\text-3i)^2\)
\(7 \boldcdot 4i\)
\((5+4i) - (\text-3 + 2i)\)
Let \(m=(7-2i)\) and \(k=3i\). Write each expression in the form \(a+bi\), where \(a\) and \(b\) are real numbers.