The equation x2 − px + q = 0, p, q ∈ R has on real root if :

According to question , we can say that
The equation x² − px + q = 0, p, q ∈ R has no real root
On comparing with quadratic eq. Ax² + Bx + C = 0 , we get
∴ A =1, B= - p, C = q
Now ,we have B² < 4AC
⇒ ( - P )² < 4 x 1 x q
⇒ p² < 4q.
Hence , option B is correct answer .