Question

An odd degree equation has at least one......​

Answer 1

Answer:

An odd degree equation has at least one real root

Explanation:

Here is a simple logical explanation for the above statement:-

We know that:

1) A polynomial f(x) of degree n, has n roots

2) Roots can be real or imaginary (Complex)

3) Complex (imaginary) roots always appear in conjugate pairs

Hence in case of odd degree equation, for eg: 3

It will have 3 roots and those three roots can be :

1) All real

2) 2 imaginary and 1 real, etc

But in case of even degree equation for eg: 4

1) It will have either all roots real

2) It can have 2 imaginary roots and 2 real

3) 4 imaginary roots

Thus,

Hence as the imaginary roots appear in pairs, an odd degree equation will always have one real root