I wonder if anyone can answer my question posted to the top-rated solution?
In case the link doesn't work, the given solution said:
"Let p(x)=x4−2x3−9x2+2x+8 and q(x)=ax+b. By sketching the graph of p, we can easily see that the only way that q can be tangent to p in two distinct points is if q is right at the bottom of p, touching each 2 down-humps in a different point, let us say, c and d.
Now let us sketch r(x)=p(x)−q(x). Because q is right at the bottom of p, the difference p(x)−q(x) is always positive, except for x=c and x=d, which make it go to zero. Therefore, r is a polynomial with only 2 real roots c and d. Furthermore, r is always positive when we get closer to c and to d, which means both have multiplicity 2 or greater."
and I am looking for explanation of the last sentence.