91Ó°ÊÓ

$$\text { In Exercises } 29-40, \text { find all real roots of the polynomial.}$$ $$x^{4}-48 x^{3}-101 x^{2}+49 x+50$$

Solve the inequality. Find exact solutions when possible and approximate ones otherwise. $$\frac{x-2}{x-1} < 1$$

In Exercises \(1-54,\) perform the indicated operation and write the result in the form \(a+b i\). $$\sqrt{-14}$$

Find a polynomial f(x) with real coefficients that satisfies the given conditions. Some of these problems have many correct answers. Degree \(6 ;\) roots 0 (of multiplicity 3 ) and \(3,1+i, 1-i,\) each of multiplicity 1.

Solve the inequality. Find exact solutions when possible and approximate ones otherwise. $$\frac{-x+5}{2 x+3} \geq 2$$

Use the Factor Theorem to determine whether or not \(h(x)\) is a factor of \(f(x)\) $$h(x)=x-1 / 2 ; \quad f(x)=2 x^{4}+x^{3}+x-3 / 4$$

$$\text { In Exercises } 29-40, \text { find all real roots of the polynomial.}$$ $$3 x^{7}+8 x^{6}-13 x^{5}-36 x^{4}-10 x^{3}+21 x^{2}+41 x+10$$

Find a polynomial f(x) with real coefficients that satisfies the given conditions. Some of these problems have many correct answers. Degree 6; roots include \(i\) (of multiplicity 2) and 3.

If the vertex of the parabola \(f(x)=-x^{2}+b x+8\) has second coordinate 17 and is in the second quadrant, find \(b\)

In Exercises \(1-54,\) perform the indicated operation and write the result in the form \(a+b i\). $$\sqrt{-800}$$