Chapter 2

Solve the quadratic equation by factoring. Check your solutions in the original equation. $$9 x^{2}-21 x=0$$

Find real numbers \(a\) and \(b\) such that the equation is true. $$(a+6)+2 b i=6-5 i$$

Find the \(x\) - and \(y\) -intercepts of the graph of the equation, if possible. $$y=4-x^{2}$$

Determine whether each value of \(x\) is a solution of the equation. Values (a) \(x=4\) (b) \(x=0\) (c) \(x=-19\) (d) \(x=16\) Equation $$\frac{\sqrt[3]{x-8}}{3}=-1$$

(a) create a scatter plot of the data, (b) draw a line of fit that passes through two of the points, and (c) use the two points to find an equation of the line. (-3,-3),(3,4),(1,1),(3,2),(4,4),(-1,-1)

Find all solutions of the equation algebraically. Use a graphing utility to verify the solutions graphically. $$x^{3}+5=5 x^{2}+x$$

Solve the quadratic equation by factoring. Check your solutions in the original equation. $$x^{2}-10 x+21=0$$

Write the complex number in standard form. $$4+\sqrt{-9}$$

Determine whether the equation is an identity, a conditional equation, or a contradiction. $$2(x-1)=2 x-2$$

(a) create a scatter plot of the data, (b) draw a line of fit that passes through two of the points, and (c) use the two points to find an equation of the line. $$(-2,3),(-2,4),(-1,2),(1,-2),(0,0),(0,1)$$

Find all solutions of the equation algebraically. Use a graphing utility to verify the solutions graphically. $$x^{4}-2 x^{3}=16+8 x-4 x^{3}$$

Solve the quadratic equation by factoring. Check your solutions in the original equation. $$x^{2}-10 x+9=0$$

Write the complex number in standard form. $$7-\sqrt{-25}$$

Determine whether the equation is an identity, a conditional equation, or a contradiction. $$-5(x-1)=-5(x+1)$$

(a) create a scatter plot of the data, (b) draw a line of fit that passes through two of the points, and (c) use the two points to find an equation of the line. $$(0,2),(-2,1),(3,3),(1,3),(4,4)$$

Solving an Equation of Quadratic Type In Exercises 13-16, find all solutions of the equation algebraically. Check your solutions. $$x^{4}-4 x^{2}+3=0$$

Determine whether each value of \(x\) is a solution of the inequality. Inequality \(5 x-12>0\) Values (a) \(x=3\) (b) \(x=-3\) (c) \(x=\frac{5}{2}\) (d) \(x=\frac{3}{2}\)

Solve the quadratic equation by factoring. Check your solutions in the original equation. $$x^{2}-8 x+16=0$$

Find the \(x\) - and \(y\) -intercepts of the graph of the equation, if possible. $$y=\frac{4 x-8}{x}$$

Determine whether the equation is an identity, a conditional equation, or a contradiction. $$(x+3)(x-5)=x^{2}-2(x+7)$$

(a) create a scatter plot of the data, (b) draw a line of fit that passes through two of the points, and (c) use the two points to find an equation of the line. $$(3,2),(2,3),(1,5),(4,0),(5,0)$$

Solving an Equation of Quadratic Type In Exercises 13-16, find all solutions of the equation algebraically. Check your solutions. $$x^{4}-5 x^{2}-36=0$$

Determine whether each value of \(x\) is a solution of the inequality. Inequality $$-5<2 x-1 \leq 1$$ Values (a) 2 (b) -2 (c) 0 (d) \(-\frac{1}{2}\)

Solve the quadratic equation by factoring. Check your solutions in the original equation. $$4 x^{2}+12 x+9=0$$

Write the complex number in standard form. $$-3$$

Find the \(x\) - and \(y\) -intercepts of the graph of the equation, if possible. $$y=\frac{3 x-1}{4 x}$$

Determine whether the equation is an identity, a conditional equation, or a contradiction. $$x^{2}-8 x+5=(x-4)^{2}-11$$

(a) create a scatter plot of the data, (b) draw a line of fit that passes through two of the points, and (c) use the two points to find an equation of the line. $$(0,7),(3,2),(6,0),(4,3),(2,5)$$

Solving an Equation of Quadratic Type In Exercises 13-16, find all solutions of the equation algebraically. Check your solutions. $$36 t^{4}+29 t^{2}-7=0$$

Determine whether each value of \(x\) is a solution of the inequality. Inequality $$-1<\frac{3-x}{2} \leq 1$$ Values (a) \(x=-1\) (b) \(x=\sqrt{5}\) (c) \(x=1\) (d) \(x=5\)

Solve the quadratic equation by factoring. Check your solutions in the original equation. $$3 x^{2}=8-2 x$$

Write the complex number in standard form. $$-8 i-i^{2}$$

Find the \(x\) - and \(y\) -intercepts of the graph of the equation, if possible. $$x y-2 y-x+1=0$$

Determine whether the equation is an identity, a conditional equation, or a contradiction. $$(x+6)^{2}=(x+8)(x+2)$$

(a) create a scatter plot of the data, (b) draw a line of fit that passes through two of the points, and (c) use the two points to find an equation of the line. $$(3,4),(2,2),(5,6),(1,1),(0,2)$$

Solving an Equation of Quadratic Type In Exercises 13-16, find all solutions of the equation algebraically. Check your solutions. $$4 x^{4}-65 x^{2}+16=0$$

Determine whether each value of \(x\) is a solution of the inequality. Inequality $$|x-10| \geq 3$$ Values (a) \(x=13\) (b) \(x=-1\) (c) \(x=14\) (d) \(x=8\)

Solve the quadratic equation by factoring. Check your solutions in the original equation. $$2 x^{2}=19 x+33$$

Find the \(x\) - and \(y\) -intercepts of the graph of the equation, if possible. $$x y-x+4 y=3$$

Determine whether the equation is an identity, a conditional equation, or a contradiction. $$(x+1)(x-5)=(x+3)(x-1)$$

Find all solutions of the equation algebraically. Check your solutions. $$3 \sqrt{x}-10=0$$

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solution graphically. $$6 x>42$$

Solve the quadratic equation by factoring. Check your solutions in the original equation. $$-x^{2}-11 x=28$$

Use a graphing utility to graph the equation and approximate any \(x\) - and \(y\) -intercepts. Verify your results algebraically. $$y=3(x-2)-5$$

Write the complex number in standard form. $$(\sqrt{-16})^{2}+5$$

Determine whether the equation is an identity, a conditional equation, or a contradiction. $$3+\frac{1}{x+1}=\frac{4 x}{x+1}$$

Find all solutions of the equation algebraically. Check your solutions. $$3 \sqrt{x}-6=0$$

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solution graphically. $$-10 x \leq 40$$

Solve the quadratic equation by factoring. Check your solutions in the original equation. $$-x^{2}-11 x=30$$

Use a graphing utility to graph the equation and approximate any \(x\) - and \(y\) -intercepts. Verify your results algebraically. $$y=4(x+3)-2$$