4.4 Polynomial equations practice 2

For what value of [math]c[/math] will three of the four real roots of [math]x^4+5x^3-x^2-21x+c=0[/math] be shared by the polynomial [math]x^3+2x^2-5x-6=0[/math]?

Consider a polynomial equation [math]x^4+ax^3+bx^2+cx+12[/math] where [math]a, b, c[/math] are integers. Suppose the equation has four distinct rational solutions. Find [math]a+b+c[/math]. If you have two or more answers, write the biggest one.

How many integer solutions are there to the equation [math]14x^4-8x^3+28x=3[/math]?

The greatest root of the equation [math]2x^3-3x^2-11x+6=0[/math] is

Which of the following is a zero of the function [math]f(x)=2x^3-11x^2+11x-3[/math]?

Which of the following numbers is/are the solution(s) to the equation [math]4x^5+16x^4+15x^3+8x^2-4x-3=0[/math] given [math]x=-3[/math] and [math]x=\pm\frac{1}{2}[/math] are three of the solutions?