If $\alpha ,\beta ,\gamma ,\delta$  are the roots of $x^4-10x^3+35x^2-50x+24=0$  which are in A.P. where $\alpha =1$  then common difference of that A.p is $\left(\alpha <\beta <\gamma <\delta \right)$

Roots are in A.P $\Rightarrow \alpha ,\beta ,\gamma ,\delta \left(\alpha <\beta <\gamma <\delta \right)$

Where $\alpha =1$

Roots are in A.P$\Rightarrow 1,1+d,1+2d,1+3d$

$\Rightarrow 4+6d=10\left[\left(\alpha +\beta +\gamma +\delta \right)=-\left(-10\right)\right]$

$\Rightarrow 6d=6$

$\Rightarrow d=1$

$\therefore$ Common difference is 1.