If(a²-14a+ 13)x² +(a + 2)x - 2=0 does not have two distinct real roots, and maximum value of a² - 15a is k, then  IKI is equal to

Let $\mathrm{f}\left(\mathrm{x}\right)=\left({\mathrm{a}}^2-14\mathrm{a}+13\right){\mathrm{x}}^2+(\mathrm{a}+2)\mathrm{x}-2$
Equation have no distinct real roots.
$\therefore \text{ Either }\mathrm{f}\left(\mathrm{x}\right)\ge 0\text{ or }\mathrm{f}\left(\mathrm{x}\right)\le 0\mathrm{\forall }\mathrm{x}\in \mathrm{R}$
$\text{ But }\mathrm{f}\left(0\right)=-2<0$
$\therefore \mathrm{f}\left(0\right)\le 0\mathrm{\forall }\mathrm{x}\in \mathrm{R}$
$\text{ So, }\mathrm{f}(-1)\le 0$
$\begin{array}{r}\Rightarrow \left({\mathrm{a}}^2-14\mathrm{a}+13\right)-(\mathrm{a}+2)-2\le 0\\ \Rightarrow {\mathrm{a}}^2-15\mathrm{a}+9\le 0\\ \Rightarrow {\mathrm{a}}^2-15\mathrm{a}\le -9\end{array}$
So, the maximum value of ${\mathrm{a}}^2-15\mathrm{a}=-9$
$\therefore |-9|=9$