Question

if p(x) is a non zero polynomial p(k²)=0, where k is a real number then what is the least degree of p(x)

Answer 1

In the attachment I have answered this problem.

The least degree of P(x) is 1

I hope this answer help you

Answer 2

Answer: 1

Step-by-step explanation:

The factor theorem says that a polynomial has a factor if and only if it  is a root.

Given: p(x) is a non zero polynomial such that $p(k^2)=0$, where k is a real number .

It means $k^2$ is a root of the p(x)

By factor theorem, $(x-k^2)$ is a factor of the polynomial, which is a polynomial itself.

$Let\ g(x)=(x-k^2)\\\\g(k^2)=(k^2-k^2)=0$

Here degree of g(x) is 1.

But g(x) satisfies all the properties for p(x), so p(x) can be $p(x)=(x-k^2)$

Hence, the least degree of p(x)=1