Đáp án:
$\begin{array}{l}
a)m = 3\\
\Rightarrow {x^2} + 3x - 2m + 3 = 0\\
\Rightarrow {x^2} + 3x - 3 = 0\\
\Rightarrow {x^2} + 2.x.\dfrac{3}{2} + \dfrac{9}{4} - \dfrac{{21}}{4} = 0\\
\Rightarrow {\left( {x + \dfrac{3}{2}} \right)^2} = \dfrac{{21}}{4}\\
\Rightarrow x = \dfrac{{ - 3 \pm \sqrt {21} }}{2}\\
\text{Vậy}\,x = \dfrac{{ - 3 \pm \sqrt {21} }}{2}\\
b)\text{pt có nghiệm kép thì}\\
\Rightarrow \Delta = 0\\
\Rightarrow {3^2} - 4.\left( { - 2m + 3} \right) = 0\\
\Rightarrow 9 + 8m - 12 = 0\\
\Rightarrow 8m = 3\\
\Rightarrow m = \dfrac{3}{8}\\
\text{Vậy}\,m = \dfrac{3}{8}\\
c)x = - 3\\
\Rightarrow {\left( { - 3} \right)^2} + 3.\left( { - 3} \right) - 2m + 3 = 0\\
\Rightarrow 9 - 9 - 2m + 3 = 0\\
\Rightarrow m = \dfrac{3}{2}\\
\text{Vậy}\,m = \dfrac{3}{2}\\
d)\Delta > 0\\
\Rightarrow 8m - 3 > 0\\
\Rightarrow m > \dfrac{3}{8}\\
\text{Vậy}\,m > \dfrac{3}{8}
\end{array}$
