First slide

Theory of expressions

Question

The smallest value of $x^{2} - 3 x + 3$ in the interval $[- 3, \frac{3}{2}]$ is

Easy

A

$\frac{3}{4}$
B

5
C

$-$ 15
D

$-$ 20

Solution

Minimum value = $\frac{4 a c - b^{2}}{4 a}$ (If a>0,then the minimum value of $a x^{2} + b x + c$ is $\frac{4 a c - b^{2}}{4 a}, a t x = \frac{- b}{2 a}, \forall x \in ℝ$ )
$x = \frac{- b}{2 a} = \frac{3}{2 (1)} = \frac{3}{2} \in [- 3, \frac{3}{2}] m i n i m u m v a l u e = \frac{4 (1) (3) - 9}{4} = \frac{3}{4}$

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