Problem 3
Without solving each equation, find the sum and product of the roots. \(x^{2}+x+1=0\)
Problem 7
Without solving each equation, find the sum and product of the roots. \(3 x^{2}-6 x+4=0\)
Problem 8
In \(3-18,\) write each number in terms of \(i\) $$ \sqrt{-8} $$
Problem 10
In \(3-18,\) write each number in terms of \(i\) $$ -\sqrt{-72} $$
Problem 10
In \(3-14\) , use the quadratic formula to find the roots of each equation. Irrational roots should be written in simplest radical form. $$ x^{2}+2 x=4 $$
Problem 11
In \(3-14\) , use the quadratic formula to find the roots of each equation. Irrational roots should be written in simplest radical form. $$ 3 x^{2}-5 x+2=0 $$
Problem 11
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. $$ f(x)=x^{2}+4 x+2 $$
Problem 12
Without solving each equation, find the sum and product of the roots. \(x^{2}-\frac{1}{4}=0\)
Problem 14
In \(3-18,\) find all roots of each given function by factoring or by using the quadratic formula. $$ \mathrm{f}(x)=x^{5}-x^{4}-2 x^{3} $$
Problem 22
In \(9-26,\) solve each quadratic equation by completing the square. Express the answer in simplest radical form. $$ 2 x^{2}-6 x+3=0 $$