Question

State true or false.
If a polynomial p(x) is of degree “n”, the graph of the polynomial should cut the X axis at “n” points.

• A. True
• B. False

Answer 1

The correct option is B False

Any polynomial of degree ‘n’ has at most ‘n’ real roots that means graph of the polynomial cut the X-axis maximum at n points.
For example $x^2-2x+1=0$ has two roots (both coincident) but the graph of $y=x^2-2x+1$ touches the X-axis in just one point.

Thus, it is not necessary that a polynomial of degree n must cut the X axis at n points