Question

Prove 3x^3-4x^2+5x-2 has no rational roots and show that irrational roots are between x=0 an x=1.

Answer 1

show that \(f(0)=-2\) is negative and \(f(1)=2\) is positive, so there must be a zero in between 0 and 1 (polynomial is continuous, take on all values between -2 and 2, including 0)

Answer 2

if it had a rational 0, it must be of the for \(\frac{p}{q}\) where \(p\) divides 2 and \(q\) divides 3
i guess you could check those and say that none work