The number of distinct real roots of x4−4x3+12x2+x−1=0 is

Let f(x)=x4−4x3+12x2+x−1∴ f′(x)=4x3−12x2+24x+1⇒ f′′(x)=12x2−24x+24=12x2−2x+2=12(x−1)2+1>0i.e, f′′(x)  has no real rootsHence, f(x)  has maximum two distinct real roots, where f(0)=−1