Question

If one of the root of the equation `x^2+px+q=0` is the square of another then what is the relation between p and q?

Answer 1

See below.

Explanation:

We are told that `x^2+px+q=0`, and we are asked to find the relationship between `p` and `q`. In order to approach this problem, you will need to know the following:

The square of the linear factor `(x+a)` can be written as `(x+a)^2` or `x^2+2ax+a^2`.

Based on this information, we know that `2a=p`, and `a^2=q`. Therefore, `a=sqrt(q)`. We can use substitution to find the relationship between `p` and `q`:

`2a=p`

`2(sqrt(q))=p`

`2sqrt(q)=p`

`(p/2)=sqrt(q)`

`(p/2)^2=(sqrt(q))^2`

`q=p^2/4`

I hope that helps!