Question

The factors of 2x^2-x+p are rational for what value of p?

Answer 1

We have 2x²-x+p = 0

roots are

x= {1+√(1-4x2p)}/4 , {1-√(1-4x2p)}/4

x= {1+√(1-8p)}/4 , {1-√(1-8p)}/4

for factors to be rational p should be 1/8

i.e p=1/8