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  4. Let k be an integer and p is a prime such that the quadratic equation x 2+ kx + p =0 has two distinct positive integer solutions. The value of (k+p) equals

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Q. Let $k$ be an integer and $p$ is a prime such that the quadratic equation $x ^2+ kx + p =0$ has two distinct positive integer solutions. The value of $(k+p)$ equals

Complex Numbers and Quadratic Equations

Solution:

Let $r _1$ and $r _2$ are two integral solutions
$r_1+r_2=-k \text { and } r_1 r_2=p$
since $p$ is prime hence either $r _1=1$ or $r _2=1$
let $r_1=1 ; r_2=p$
$1+p=-k$
$ \Rightarrow k+p=-1$