Question

Select the correct answer from the drop-down menu. Find the polynomial. {5} is the solution set of.

1. x^2-5x+25=0
2. x^2+10x+25=0
3. x^2-10x+25=0
4. x^2+5x+25=0

Answer 1

3.
`x^2-10x+25=0`

Explanation:

All the polynomials in the given option are quadratic.

By the fundamental theorem of algebra, the quadratic polynomial has two roots.

Since the solution set is given as {5}, the quadratic has a repeated root.

In other words the root has a multiplicity of 2.

Hence we have the equation:

`x=5`, multiplicity 2

This implies that;

`(x-5)^2=0`

We expand to obtain;

`x^2-5x-5x+25=0`

`x^2-10x+25=0`

The correct choice is the third option.