Use De Moivre’s Theorem to compute the following:
29%2B8isin%284%5Cpi%2F5%29%29%7D%20" id="TexFormula1" title="\sqrt[3]{(8cos(4 \pi /5)+8isin(4\pi/5))} " alt="\sqrt[3]{(8cos(4 \pi /5)+8isin(4\pi/5))} " align="absmiddle" class="latex-formula">
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Answer:
When a graph has 2 x-intercepts, it will have positive discriminant & when a graph has NO x-intercepts, it will have negative discriminant.
Step-by-step explanation:
In a quadratic equation, the discriminant is the value of . This is "under the square root sign" when solving using quadratic formula.
Thus, there can be 3 possibilities:
1. Discriminant is 0 ( 2 equal real roots - meaning 1 touching point at the x-axis in the graph)
2. Discriminant can be positive ( 2 distinct real roots - meaning 2 cutting point in the x axis)
3. Discriminant can be negative ( 2 complex roots - meaning NO cutting point in x-axis)
Thus, when a graph has 2 x-intercepts, it will have positive discriminant & when a graph has NO x-intercepts, it will have negative discriminant.