Question

Find the value of p for which the quadratic equation x²-2px+1=0 had no real roots.

Answer 1

We need b^2 - 4ac < 0.

Here a = 1 , b = -2p and c = 1.

So (-2p)^2 - 4 < 0

4p^2 - 4 < 0

p^2 - 1 < 0

p^2 < 1

=> -1 < p < 1

So p can be anything in between (-1 , 1) for example p=0 also works.