Question

A polynomial is to he constructed that will touch the x axis at most 4 times. What is the minimum degree of the polynomial?

Answer 1

at most 4 times
hmm
where it touches is when y=0
so just have lots of zeroes
y=(x-r1) is a zero
so 4 zeroes is
y=(x-r1)(x-r2)(x-r3)(x-r4)
if we expand it it is degree 4

minimum degree is 4th