Chapter 6

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. $$3 x^{2}+4 x=2$$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$2 n^{2}-n-15=0$$

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. $$x^{2}+x-30=0$$

Add or subtract as indicated. $$(6+3 i)+(4+5 i)$$

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

Solve each quadratic equation using the method that seems most appropriate to you. $$28-x-2 x^{2}=0$$

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. $$2 x^{2}-6 x=-1$$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$3 n^{2}+n-14=0$$

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. $$x^{2}-8 x-48=0$$

Add or subtract as indicated. $$(5+2 i)+(7+10 i)$$

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

Solve each quadratic equation using the method that seems most appropriate to you. $$(x-2)(x+9)=-10$$

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$x^{2}+2 x-1=0$$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$3 n^{2}+7 n-6=0$$

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. $$x^{2}-19 x+84=0$$

Add or subtract as indicated. $$(-8+4 i)+(2+6 i)$$

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

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

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$x^{2}+4 x-1=0$$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$2 n^{2}+7 n-4=0$$

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. $$x^{2}-21 x+104=0$$

Add or subtract as indicated. $$(5-8 i)+(-7+2 i)$$

Solve each inequality and graph its solution set on a number line. $$\frac{x+1}{x-2}>0$$

Solve each quadratic equation using the method that seems most appropriate to you. $$2 x^{2}-4 x+7=0$$

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$n^{2}+5 n-3=0$$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$n(n+6)=160$$

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. $$2 x^{2}+19 x+24=0$$

Add or subtract as indicated. $$(3+2 i)-(5+7 i)$$

Solve each inequality and graph its solution set on a number line. $$\frac{x-1}{x+2}>0$$

Solve each quadratic equation using the method that seems most appropriate to you. $$3 x^{2}-2 x+8=0$$

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

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$n(n-6)=216$$

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. $$4 x^{2}+29 x+30=0$$

Add or subtract as indicated. $$(1+3 i)-(4+9 i)$$

Solve each inequality and graph its solution set on a number line. $$\frac{x-3}{x+2}<0$$

Solve each quadratic equation using the method that seems most appropriate to you. $$x^{2}-18 x+15=0$$

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$a^{2}-8 a=4$$

Use the method of completing the square to solve each quadratic equation. $$x^{2}+4 x-2=0$$

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. $$15 x^{2}+29 x-14=0$$

Add or subtract as indicated. $$(-7+3 i)-(5-2 i)$$

Solve each inequality and graph its solution set on a number line. $$\frac{x+2}{x-4}<0$$

Solve each quadratic equation using the method that seems most appropriate to you. $$x^{2}-16 x+14=0$$

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

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

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. $$24 x^{2}+x-10=0$$

Add or subtract as indicated. $$(-8+4 i)-(9-4 i)$$

Solve each inequality and graph its solution set on a number line. $$\frac{2 x-1}{x} \geq 0$$

Solve each quadratic equation using the method that seems most appropriate to you. $$20 y^{2}+17 y-10=0$$

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$n^{2}+5 n+8=0$$

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