Chapter 6

Solve each inequality. $$(x+1)(x-3)^{2}>0$$

Solve each equation. $$3 x^{4}-35 x^{2}+72=0$$

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$4 x^{2}-2 x=3$$

Use the method of completing the square to solve each quadratic equation. $$3 n^{2}-6 n+5=0$$

Write each of the following in terms of \(i\) and simplify. For example, $$ \sqrt{-20}=i \sqrt{20}=i \sqrt{4} \sqrt{5}=2 i \sqrt{5} $$ $$\sqrt{-75}$$

Solve each inequality. $$(x-4)^{2}(x-1) \leq 0$$

Solve each equation. $$5 x^{4}-32 x^{2}+48=0$$

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$6 x^{2}-4 x=3$$

Use the method of completing the square to solve each quadratic equation. $$3 x^{2}+12 x-2=0$$

Write each of the following in terms of \(i\) and simplify. For example, $$ \sqrt{-20}=i \sqrt{20}=i \sqrt{4} \sqrt{5}=2 i \sqrt{5} $$ $$\sqrt{-63}$$

Solve each inequality. $$4-x^{2}<0$$

Solve each equation. $$3 x^{4}+17 x^{2}+20=0$$

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$5 x^{2}-13 x=0$$

Use the method of completing the square to solve each quadratic equation. $$3 x^{2}+5 x-1=0$$

Write each of the following in terms of \(i\) and simplify. For example, $$ \sqrt{-20}=i \sqrt{20}=i \sqrt{4} \sqrt{5}=2 i \sqrt{5} $$ $$3 \sqrt{-28}$$

Solve each inequality. $$2 x^{2}-18 \geq 0$$

Solve each equation. $$4 x^{4}+11 x^{2}-45=0$$

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$7 x^{2}+12 x=0$$

Use the method of completing the square to solve each quadratic equation. $$2 x^{2}+7 x-3=0$$

Write each of the following in terms of \(i\) and simplify. For example, $$ \sqrt{-20}=i \sqrt{20}=i \sqrt{4} \sqrt{5}=2 i \sqrt{5} $$ $$5 \sqrt{-72}$$

Solve each inequality. $$4\left(x^{2}-36\right)<0$$

Solve each equation. $$6 x^{4}-29 x^{2}+28=0$$

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$3 x^{2}=5$$

Solve each quadratic equation using the method that seems most appropriate. $$x^{2}+8 x-48=0$$

Write each of the following in terms of \(i\) and simplify. For example, $$ \sqrt{-20}=i \sqrt{20}=i \sqrt{4} \sqrt{5}=2 i \sqrt{5} $$ $$-2 \sqrt{-80}$$

Solve each inequality. $$-4\left(x^{2}-36\right) \geq 0$$

Solve each equation. $$6 x^{4}-31 x^{2}+18=0$$

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$4 x^{2}=3$$

Solve each quadratic equation using the method that seems most appropriate. $$x^{2}+5 x-14=0$$

Write each of the following in terms of \(i\) and simplify. For example, $$ \sqrt{-20}=i \sqrt{20}=i \sqrt{4} \sqrt{5}=2 i \sqrt{5} $$ $$-6 \sqrt{-27}$$

Solve each inequality. $$5 x^{2}+20>0$$

Set up an equation and solve each problem. Find two consecutive whole numbers such that the sum of their squares is 145 .

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$6 t^{2}+t-3=0$$

Solve each quadratic equation using the method that seems most appropriate. $$2 n^{2}-8 n=-3$$

Write each of the following in terms of \(i\) and simplify. For example, $$ \sqrt{-20}=i \sqrt{20}=i \sqrt{4} \sqrt{5}=2 i \sqrt{5} $$ $$12 \sqrt{-90}$$

Solve each inequality. $$-3 x^{2}-27 \geq 0$$

Set up an equation and solve each problem. Find two consecutive odd whole numbers such that the sum of their squares is 74 .

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$2 t^{2}+6 t-3=0$$

Solve each quadratic equation using the method that seems most appropriate. $$3 x^{2}+6 x=1$$

Write each of the following in terms of \(i\) and simplify. For example, $$ \sqrt{-20}=i \sqrt{20}=i \sqrt{4} \sqrt{5}=2 i \sqrt{5} $$ $$9 \sqrt{-40}$$

Solve each inequality. $$x^{2}-2 x \geq 0$$

Set up an equation and solve each problem. Two positive integers differ by 3 , and their product is 108 . Find the numbers.

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$n^{2}+32 n+252=0$$

Solve each quadratic equation using the method that seems most appropriate. $$(3 x-1)(2 x+9)=0$$

Write each of the following in terms of \(i\), perform the indicated operations, and simplify. For example, $$ \begin{aligned} \sqrt{-3} \sqrt{-8} &=(i \sqrt{3})(i \sqrt{8}) \\ &=i^{2} \sqrt{24} \\ &=(-1) \sqrt{4} \sqrt{6} \\ &=-2 \sqrt{6} \end{aligned} $$ $$\sqrt{-4} \sqrt{-16}$$

Solve each inequality. $$2 x^{2}+6 x<0$$

Set up an equation and solve each problem. Suppose that the sum of two numbers is 20 , and the sum of their squares is 232 . Find the numbers.

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$n^{2}-4 n-192=0$$

Solve each quadratic equation using the method that seems most appropriate. $$(5 x+2)(x-4)=0$$

Write each of the following in terms of \(i\), perform the indicated operations, and simplify. For example, $$ \begin{aligned} \sqrt{-3} \sqrt{-8} &=(i \sqrt{3})(i \sqrt{8}) \\ &=i^{2} \sqrt{24} \\ &=(-1) \sqrt{4} \sqrt{6} \\ &=-2 \sqrt{6} \end{aligned} $$ $$\sqrt{-81} \sqrt{-25}$$