Prove, by the method of contradiction, that the equation
xn+an−1xn−1+⋯+a1x+a0=0,
in which all the coefficients ai are integers, cannot have a rational root, unless that root is an integer. Deduce that any integral root must be a divisor of a0 and hence find all rational roots of
(a) x4+6x3+4x2+5x+4=0,
(b) x4+5x3+2x2−10x+6=0.