Question

Let the roots of $x^2-3x+1=0$ be $r$ and $s$. Then the expression $r^2+s^2$ is

• A. A positive integer
• B. A positive fraction greater than $1$
• C. A positive fraction less than $1$
• D. An irrational number
• E. An imaginary number

Answer 1

The correct option is A A positive integer

$x^2-3x+1=0$

Roots are $r\&s$

$r+s=3$

$rs=1$

$r^2+s^2=(r+s{)}^2-2rs$

$=3^2-2.1$

$=9-2=7$

So a positive integer