Question

The value of k for which the polynomial $x^3+10x^2+kx+1$ is continuous for all values of x is

• A. K = 0
• B. k = 1
• C. k = 10
• D. k can take value of any real number

Answer 1

The correct option is D

k can take value of any real number

A polynomial is always continuous whatever be the coefficients be. This is because there are no points of breakage along the curve. The given equation is a cubic polynomial who graph will take the below shape.

Here when we change coefficients only the shape or position of the plot changes. Beside that no extra breaks will appear.