I was working on some solving equations in preparation for university, and came across a few that I just could not understand how to do them. I have the answers, but do not know how to get to them, how painful....
1. Find a cubic function of x whose graph has x-intercepts equal to -1 and 2, and in which f(0)=6 and f(3)=12.
2. The roots of the equation x^2+px+1=0 are a and b, and the roots of the equation x^2-9x+q=0 are a+2b and 2a+b. (a and b are greek symbols).
Answer: p=-3, q=19
3. If the roots of the equation x^3-15x^2+cx-105, are a, a+b, and a-b, determine the values of a,b, and c.
Answer: a=5, b=+2,-2 c=71
Thanks in advance!