Can a degree 3 polynomial intersect a degree 4 polynomial in

Can a degree 3 polynomial intersect a degree 4 polynomial in exactly five points? Explain.

Solution

Let, f(x) be degree 3 polynomial

ANd g(x) be degree 4 polynoimal

So points of intersection are given by roots of the polynomial

h(x)=g(x)-f(x)

But, h(x) is degree 4 polynoimal and hence has atmost 4 roots

So there can be atmost 4 points of intersection