Question

Find the value of p for which the quadratic equation $x^2-2px+1=0$ has no real roots.

Answer 1

Given equation: x² − 2px + 1 = 0
Here, a = 1, b = − 2p , c = 1
For no real roots, b² − 4ac < 0
b² − 4ac = (−2p)² − (4 ×1 × 1)
⇒ 4p² − 4 < 0
⇒ 4(p² − 1) < 0
⇒ (p² − 1) < 0 [ Since 4 < 0, which is not possible]
⇒ −1 < p < 1