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Q.
The smallest value of $x^{2}-3 x+3$ in the interval $\left(-3, \frac{3}{2}\right)$ is
Complex Numbers and Quadratic Equations
Solution:
We have, $x^{2}-3 x+3$
$=\left(x-\frac{3}{2}\right)^{2}+3-\frac{9}{4}$
$=\left(x-\frac{3}{2}\right)^{2}+\frac{3}{4}$
$\therefore $ smallest value $=\frac{3}{4}$,
which lies in the interval $\left(-3, \frac{3}{2}\right)$