Chapter 5

In \(3-14,\) use the quadratic formula to find the imaginary roots of each equation. $$ x^{2}+8 x+17=0 $$

Without solving each equation, find the sum and product of the roots. \(-x^{2}+3 x+1=0\)

In \(3-17,\) find each sum or difference of the complex numbers in \(a+b i\) form. $$ (4+12 i)+(-4-2 i) $$

In \(3-18,\) write each number in terms of \(i\) $$ \sqrt{-8} $$

In \(3-14\) , use the quadratic formula to find the roots of each equation. Irrational roots should be written in simplest radical form. $$ x^{2}-8=0 $$

In \(3-8,\) complete the square of the quadratic expression. $$ x^{2}-3 x $$

In \(9-17,\) graph each system and determine the common solution from the graph. $$ \begin{array}{l}{y=x^{2}-2 x-1} \\ {y=x+3}\end{array} $$

In \(3-14,\) use the quadratic formula to find the imaginary roots of each equation. $$ x^{2}-2 x+10=0 $$

In \(3-18,\) find all roots of each given function by factoring or by using the quadratic formula. $$ f(x)=x^{4}-5 x^{2}+4 $$

Without solving each equation, find the sum and product of the roots. \(8 x+12=x^{2}\)

In \(3-17,\) find each sum or difference of the complex numbers in \(a+b i\) form. $$ (1+9 i)-(1+2 i) $$

In \(3-18,\) write each number in terms of \(i\) $$ \sqrt{-12} $$

In \(3-14\) , use the quadratic formula to find the roots of each equation. Irrational roots should be written in simplest radical form. $$ \mathfrak{x}^{2}-3 x=0 $$

In \(9-14 :\) a Sketch the graph of each function. b. From the graph, estimate the roots of the function to the nearest tenth. c. Find the exact irrational roots in simplest radical form. $$ \mathrm{f}(x)=x^{2}-6 x+4 $$

In \(3-14,\) use the quadratic formula to find the imaginary roots of each equation. $$ 4 x^{2}-4 x+5=0 $$

In \(3-18,\) find all roots of each given function by factoring or by using the quadratic formula. $$ f(x)=x^{4}+5 x^{2}+4 $$

Without solving each equation, find the sum and product of the roots. \(4 x^{2}=2 x+9\)

In \(3-17,\) find each sum or difference of the complex numbers in \(a+b i\) form. $$ (10-12 i)-(12+7 i) $$

In \(3-18,\) write each number in terms of \(i\) $$ -\sqrt{-72} $$

In \(3-14\) , use the quadratic formula to find the roots of each equation. Irrational roots should be written in simplest radical form. $$ x^{2}+2 x=4 $$

In \(9-14 :\) a Sketch the graph of each function. b. From the graph, estimate the roots of the function to the nearest tenth. c. Find the exact irrational roots in simplest radical form. $$ \mathrm{f}(x)=x^{2}-2 x-2 $$

In \(9-17,\) graph each system and determine the common solution from the graph. $$ \begin{array}{l}{-x^{2}+4 x-y-2=0} \\ {x+y=4}\end{array} $$

In \(3-14,\) use the quadratic formula to find the imaginary roots of each equation. $$ 4 x^{2}+4 x+17=0 $$

In \(3-18,\) find all roots of each given function by factoring or by using the quadratic formula. $$ f(x)=x^{4}-81 $$

Without solving each equation, find the sum and product of the roots. \(2 x^{2}-8=5 x\)

In \(9-14\) : a. For each given value of the discriminant of a quadratic equation with rational coefficients, determine if the roots of the quadratic equation are \((1)\) rational and unequal, \((2)\) rational and equal, \((3)\) irrational and unequal, or \((4)\) not real numbers. b. Use your answer to part a to determine the number of \(x\) -intercepts of the graph of the corresponding quadratic function. 0

In \(3-17,\) find each sum or difference of the complex numbers in \(a+b i\) form. $$ (0+3 i)+(0-3 i) $$

In \(3-18,\) write each number in terms of \(i\) $$ 5 \sqrt{-27} $$

In \(3-14\) , use the quadratic formula to find the roots of each equation. Irrational roots should be written in simplest radical form. $$ 3 x^{2}-5 x+2=0 $$

In \(9-14 :\) a Sketch the graph of each function. b. From the graph, estimate the roots of the function to the nearest tenth. c. Find the exact irrational roots in simplest radical form. $$ f(x)=x^{2}+4 x+2 $$

In \(9-17,\) graph each system and determine the common solution from the graph. $$ \begin{array}{l}{y=-x^{2}+6 x-1} \\ {y=x+3}\end{array} $$

In \(3-14,\) use the quadratic formula to find the imaginary roots of each equation. $$ x^{2}+5=4 x $$

In \(3-18,\) find all roots of each given function by factoring or by using the quadratic formula. $$ f(x)=16 x^{4}-1 $$

Without solving each equation, find the sum and product of the roots. \(x^{2}-\frac{1}{4}=0\)

In \(3-17,\) find each sum or difference of the complex numbers in \(a+b i\) form. $$ \left(\frac{1}{2}+\frac{1}{2} i\right)+\left(\frac{1}{4}-\frac{3}{4} i\right) $$

In \(3-18,\) write each number in terms of \(i\) $$ -\frac{1}{2} \sqrt{-80} $$

In \(3-14\) , use the quadratic formula to find the roots of each equation. Irrational roots should be written in simplest radical form. $$ 4 x^{2}-x-1=0 $$

In \(9-14 :\) a Sketch the graph of each function. b. From the graph, estimate the roots of the function to the nearest tenth. c. Find the exact irrational roots in simplest radical form. $$ f(x)=x^{2}-6 x+6 $$

In \(9-17,\) graph each system and determine the common solution from the graph. $$ \begin{array}{l}{y=2 x^{2}+2 x+3} \\ {y-x=3}\end{array} $$

In \(3-14,\) use the quadratic formula to find the imaginary roots of each equation. $$ 4 x-7=x^{2} $$

In \(3-18,\) find all roots of each given function by factoring or by using the quadratic formula. $$ f(x)=x^{4}-10 x^{2}+9 $$

Without solving each equation, find the sum and product of the roots. \(x^{2}+1=0\)

In \(9-14\) : a. For each given value of the discriminant of a quadratic equation with rational coefficients, determine if the roots of the quadratic equation are \((1)\) rational and unequal, \((2)\) rational and equal, \((3)\) irrational and unequal, or \((4)\) not real numbers. b. Use your answer to part a to determine the number of \(x\) -intercepts of the graph of the corresponding quadratic function. -4

In \(3-17,\) find each sum or difference of the complex numbers in \(a+b i\) form. $$ \left(\frac{2}{3}-\frac{1}{6} i\right)+(2-i) $$

In \(3-18,\) write each number in terms of \(i\) $$ -\sqrt{-51} $$

In \(3-14\) , use the quadratic formula to find the roots of each equation. Irrational roots should be written in simplest radical form. $$ 5 x+1=2 x^{2} $$

In \(9-14 :\) a Sketch the graph of each function. b. From the graph, estimate the roots of the function to the nearest tenth. c. Find the exact irrational roots in simplest radical form. $$ f(x)=x^{2}-2 x-1 $$

In \(9-17,\) graph each system and determine the common solution from the graph. $$ \begin{array}{l}{y=2 x^{2}-6 x+5} \\ {y=x+2}\end{array} $$

In \(3-18,\) find all roots of each given function by factoring or by using the quadratic formula. $$ \mathrm{f}(x)=x^{5}-x^{4}-2 x^{3} $$

In \(3-14,\) use the quadratic formula to find the imaginary roots of each equation. $$ 2 x=x^{2}+3 $$