Let α and β are the roots of the equation x2-(p-2) x-p-1=0(p ∈ R). If α2+β2 is least, then p equals

Question

Let α and β are the roots of the equation x2-(p-2) x-p-1=0(p ∈ R). If α2+β2 is least, then p equals (A) 0 (B) 1 (C) 2 (D) 5

Tardigrade Admin · Accepted Answer

E=α2+β2=(α+β)2-2 α β=(p-2)2+2(p+1)=p2-2 p+6=(p-1)2+5 E min .=5 when p =1.

Q. Let $α$ and $β$ are the roots of the equation $x^{2} - (p - 2) x - p - 1 = 0 (p \in R)$ . If $α^{2} + β^{2}$ is least, then $p$ equals