If the roots of the equation $x^3-9x^2+23x-15=0$ are in A.P then common difference of  that A.P is

The given equation is $x^3-9x^2+23x-15=0$

Given that roots are in A.P.,

$\therefore$  the roots are $\left(a-d\right),a,\left(a+d\right)$

Sum of the roots: $\left(a-d\right)+a+\left(a+d\right)=9$

$\Rightarrow 3a=9$

$\therefore a=3$

Product of the roots : $\left(a-d\right).a.\left(a+d\right)=15$

$\Rightarrow a\left(a^2-d^2\right)=15$                        $\left(\because a=3\right)$

$\Rightarrow d=2$