If one root of equation x² + ax + 12 = 0 is 4 while the equation x² + ax + b = 0 has equal roots, then the value of b is

Since, 4 is a root of $x^2+ax+12=0$
$\begin{array}{l}\therefore \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}16+4\mathrm{a}+12=0\\ \Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\mathrm{a}=-7\end{array}$
Let the roots of the equation $x^2+ax+b=0$ be $\alpha$ and $\alpha$
$\therefore 2\mathrm{\alpha }=-\mathrm{a}\Rightarrow \mathrm{\alpha }=\frac{7}{2}$
and $\mathrm{\alpha }\cdot \mathrm{\alpha }=\mathrm{b}\Rightarrow {\left(\frac{7}{2}\right)}^2=\mathrm{b}$
$\Rightarrow \mathrm{b}=\frac{49}{4}$