Note: Discarte's Rule of Signs
No equation can have more +ve real roots than it has changes of sign from +ve to -ve, and from -ve to + ve.
And similarly, number of -ve roots of f(x) can not more than the number of changes of sign in f (- x).
Now given f(x)=(x−1)(x−3)(x−4)(x−6)+19 ⇒f(x)=x4−14x3+67x2−126x+91
Here, f(x) has four changes of sign. So the equation can not have more than four positive roots. And f(-x) has no changes of sign, so by Discarte rule, the equation have no relative roots. As f(−x)=x4+14x3+67x2+126x+91
Thus the equation have four positive roots.