If the graph of a polynomial intersects the x-axis at exactly two points, it need not be a quadratic polynomial. plaese ans.. accurately?

Question

belongs to poly

Answer 1

The polynomial intersects the x axis at the polynomial's zeroes.

If a and b are the real roots of the polynomial then p(x)=(x-a)(x-b)f(x), where f(x) has complex zeroes only.

Also ((x-a)^m)((x-b)^n)f(x) has only two zeroes (m and n are integers) when f(x) only has complex zeroes or f(x) also has at least one zero matching a or b, and its remaining zeroes are complex.