Re: Math-task
skattberg wrote:Hello everyone. First I wanna say that this is a fantastic forum. But now to my question. For some weeks my teacher gave me a math-task and I didn't really understand how I should solve the problem. So I wonder that maybe one of you can help me. The task is:
How many roots?
a) 3x^4+4x³-36x²-a=0
b) e^x=ax²
c) cos x=ax
How does the roots depend of the constant a?
please, excuse my bad english
c. For me, this is simpler to figure out graphically than algebraically. Imagine graphing the straight line y = ax and y = cos x on the same set of axes. Remember that cos(0) is 1, i.e., cos x intersects the y axis at y = 1. Also, let's assume that we don't just graph between x = 0 and 2 pi but from negative infinity to positive infinity. It is clear that even for large values of a (angles of the line approaching 90 degrees), the line will intersect the cosine graph in at least one location. Smaller values of a, however, correspond to smaller angles between line and the x axis, and as the angle becomes smaller, the line will intersect the cosine graph at more and more points on both sides of the y axis. Try sketching the two functions on a single graph and you'll see what I mean.
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