91Ó°ÊÓ

Work in a small group to solve \(a x^{2}+b x+c>0\) for \(x\) in each case. a) \(b^{2}-4 a c=0\) and \(a>0\) b) \(b^{2}-4 a c=0\) and \(a<0\) c) \(b^{2}-4 a c<0\) and \(a>0\) d) \(b^{2}-4 a c<0\) and \(a<0\) e) \(b^{2}-4 a c>0\) and \(a>0\) f) \(b^{2}-4 a c>0\) and \(a<0\)

Find all real or imaginary solutions to each equation. Use the method of your choice. $$x^{2}-6 x+10=0$$

Solve each problem. Sharing cost. The members of a flying club plan to share equally the cost of a \(\$ 200,000\) airplane. The members want to find five more people to join the club so that the cost per person will decrease by \(\$ 2000 .\) How many members are currently in the club?

Find all real or imaginary solutions to each equation. Use the method of your choice. $$x^{2}-8 x+17=0$$

Find all real or imaginary solutions to each equation. Use the method of your choice. $$2 x-5=\sqrt{7 x+7}$$

Exploration. a) Given that \(P(x)=x^{4}+6 x^{2}-27,\) find \(P(3 i)\) 8 \(P(-3 i), P(\sqrt{3}),\) and \(P(-\sqrt{3})\) b) What can you conclude about the values \(3 i,-3 i, \sqrt{3}\) and \(-\sqrt{3}\) and their relationship to each other?

Solve each problem. Traveling club. The members of a traveling club plan to share equally the cost of a \(\$ 150,000\) motorhome. If they can find 10 more people to join and share the cost, then the cost per person will decrease by \(\$ 1250 .\) How many members are there originally in the club?

Find all real or imaginary solutions to each equation. Use the method of your choice. $$\sqrt{7 x+29}=x+3$$

Cooperative learning. Work with a group to write a quadratic equation that has each given pair of solutions. a) \(3+\sqrt{5}, 3-\sqrt{5}\) b) \(4-2 i, 4+2 i\) c) \(\frac{1+i \sqrt{3}}{2}, \frac{1-i \sqrt{3}}{2}\)

Find the solutions to \(6 x^{2}+5 x-4=0 .\) Is the sum of your solutions equal to \(-\frac{b}{a}\) ? Explain why the sum of the solutions to any quadratic equation is \(-\frac{b}{a}\) (Hint: Use the quadratic formula.)