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?

1 Answer
Nov 12, 2017

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!