Chapter 6

Solve each inequality and graph its solution set on a number line. $$(x+2)(x-1)>0$$

Solve each quadratic equation using the method that seems most appropriate to you. $$x^{2}-4 x-6=0$$

First use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. Then solve the equation. $$x^{2}+4 x-21=0$$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$x^{2}-4 x-60=0$$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$x^{2}-9 x=0$$

Label each statement true or false. Every complex number is a real number.

Solve each inequality and graph its solution set on a number line. $$(x-2)(x+3)>0$$

Solve each quadratic equation using the method that seems most appropriate to you. $$x^{2}-8 x-4=0$$

First use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. Then solve the equation. $$x^{2}-3 x-54=0$$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$x^{2}+6 x-16=0$$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$x^{2}+5 x=0$$

Label each statement true or false. Every real number is a complex number.

Solve each inequality and graph its solution set on a number line. $$(x+1)(x+4)<0$$

Solve each quadratic equation using the method that seems most appropriate to you. $$3 x^{2}+23 x-36=0$$

First use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. Then solve the equation. $$9 x^{2}-6 x+1=0$$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$x^{2}-14 x=-40$$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$x^{2}=-3 x$$

Label each statement true or false. The real part of the complex number \(6 i\) is 0 .

Solve each inequality and graph its solution set on a number line. $$(x-3)(x-1)<0$$

Solve each quadratic equation using the method that seems most appropriate to you. $$n^{2}+22 n+105=0$$

First use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. Then solve the equation. $$4 x^{2}+20 x+25=0$$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$x^{2}-18 x=-72$$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$x^{2}=15 x$$

Label each statement true or false. Every complex number is a pure imaginary number.

Solve each inequality and graph its solution set on a number line. $$(2 x-1)(3 x+7) \geq 0$$

Solve each quadratic equation using the method that seems most appropriate to you. $$x^{2}-18 x=9$$

First use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. Then solve the equation. $$x^{2}-7 x+13=0$$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$x^{2}-5 x-50=0$$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$3 y^{2}+12 y=0$$

Label each statement true or false. The sum of two complex numbers is always a complex number.

Solve each inequality and graph its solution set on a number line. $$(3 x+2)(2 x-3) \geq 0$$

Solve each quadratic equation using the method that seems most appropriate to you. $$x^{2}+20 x=25$$

First use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. Then solve the equation. $$2 x^{2}-x+5=0$$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$x^{2}+3 x-18=0$$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$6 y^{2}-24 y=0$$

Label each statement true or false. The imaginary part of the complex number 7 is 0 .

Solve each inequality and graph its solution set on a number line. $$(x+2)(4 x-3) \leq 0$$

Solve each quadratic equation using the method that seems most appropriate to you. $$2 x^{2}-3 x+4=0$$

First use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. Then solve the equation. $$15 x^{2}+17 x-4=0$$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$x(x+7)=8$$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$5 n^{2}-9 n=0$$

Label each statement true or false. The sum of two complex numbers is sometimes a real number.

Solve each inequality and graph its solution set on a number line. $$(x-1)(2 x-7) \leq 0$$

Solve each quadratic equation using the method that seems most appropriate to you. $$3 y^{2}-2 y+1=0$$

First use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. Then solve the equation. $$8 x^{2}+18 x-5=0$$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$x(x-1)=30$$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$4 n^{2}+13 n=0$$

Label each statement true or false. The sum of two pure imaginary numbers is always a pure imaginary number.

Solve each inequality and graph its solution set on a number line. $$(x+1)(x-1)(x-3)>0$$

Solve each quadratic equation using the method that seems most appropriate to you. $$135+24 n+n^{2}=0$$