number theory - Constructing an irreducible polynomial of degree $2$ over $mathbb{F}_p$

I want to construct an irreducible polynomial of degree $2$ over $\mathbb{F}_p$ where $p$ is a prime that can be written as $4k+1$. My attempt is as follow: we can assume that this polynomial is of the form ${x^2} + ax + b$ for some $a,b \in {\mathbb{F}_p}$. So for all $\lambda \in {F_p}$, $p$ doesn't divide ${\lambda ^2} + a\lambda + b$. It follows that ${\lambda ^2}$ is not equal to $a\lambda + b
\bmod p$. If we can find some $a,b \in {\mathbb{F}_p}$ such that $a\lambda + b$ is a nonresidue for all $\lambda \in {F_p}$, it is ok. But I cannot. I wait your response.