1) Find the value of \(\large\frac{1}{r}+\frac{1}{t}\) if \(\left\{r,t\right\}\) is the solution set of \(\large\frac{4}{5}\normalsize{x^2-}\large\frac{2}{5}\normalsize{x=6}\).
2) Find the value of constant \(k\) if the difference between the two roots of \(x^2-7x+k=0\) is \(2\).
3) Use the most appropriate method to solve the following equation over the set of complex numbers. Leave your answer in exact form. \(7x^2-4x+10=0\)
4) Use the most appropriate method to solve the following equation over the set of complex numbers. Leave your answer in exact form. \(190=6(x-5)^2+112\)
5) Use the most appropriate method to solve the following equation over the set of complex numbers. Leave your answer in exact form. \(\large\frac{7}{9}\normalsize\left(x+6\right)^2\left(3-4x\right)=0\)
6) Find the slope of the line through points \((a^2b,a^2)\) and \((0,-ab)\) if the complex solutions of \(3x^2-4x+2=0\) are \(\{a,b\}\).
7) Factor over \(\mathbb{R}\): \(x^2+2x+3\)
8) Factor over \(\mathbb{R}\): \(4x^2+4\sqrt{3}x+3\)
9) Factor over the Integers: \(308x^2+112x-1008\)
10) Factor over \(\mathbb{C}\): \(x^2+2x+4\)
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2) Find the value of constant \(k\) if the difference between the two roots of \(x^2-7x+k=0\) is \(2\).
3) Use the most appropriate method to solve the following equation over the set of complex numbers. Leave your answer in exact form. \(7x^2-4x+10=0\)
4) Use the most appropriate method to solve the following equation over the set of complex numbers. Leave your answer in exact form. \(190=6(x-5)^2+112\)
5) Use the most appropriate method to solve the following equation over the set of complex numbers. Leave your answer in exact form. \(\large\frac{7}{9}\normalsize\left(x+6\right)^2\left(3-4x\right)=0\)
6) Find the slope of the line through points \((a^2b,a^2)\) and \((0,-ab)\) if the complex solutions of \(3x^2-4x+2=0\) are \(\{a,b\}\).
7) Factor over \(\mathbb{R}\): \(x^2+2x+3\)
8) Factor over \(\mathbb{R}\): \(4x^2+4\sqrt{3}x+3\)
9) Factor over the Integers: \(308x^2+112x-1008\)
10) Factor over \(\mathbb{C}\): \(x^2+2x+4\)
Solution Bank