Question

if (a^2 - b^2)x^2 + 2abx + (a^2 + b^2) is a linear polynomial then prove a=b

Answer 1

A linear polynomial is of the form, ax+b, where a and b are some constants.

A quadratic​ polynomial is of the form ax²+bx+c, where a,b and c are some constants.

You just need to understand the difference.

A linear polynomial has 1 as highest power of x while in a quadratic polynomial, the highest power is 2.

This means in the polynomial given in the question, the x² term should not be present, in order for the polynomial to be linear. That means the coefficient of x² must be zero.

a²-b² =0 ie,
a=b
Hence proved.