3. has roots .
That means .
So
.
Solve these three equations simultaneously for .
Hi everyone,
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.
Answer: 2x^3-5x^2-x+6
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!
Use the model (why?) and use the fact that f(0) = 6 and f(3) = 12 to get two simuatenous equations for a and b.
. Therefore:
.... (1)
.... (2)
In a similar way, . Therefore:
...... (3)
....... (4)
Solve equations (1), (2), (3) and (4) simultaneously to get p and q.
If you need more help, please show all your work and say where you get stuck.