If the roots of the equation x2−2ax+a2+a−3=0 are real and less than 3 then

# If the roots of the equation ${x}^{2}-2ax+{a}^{2}+a-3=0$ are real and less than 3 then

1. A

$a<2$

2. B

$2\le a\le 3$

3. C

$3

4. D

$a>4$

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### Solution:

$D\ge 0⇒12-4a\ge 0$

$f\left(3\right)>0⇒{a}^{2}-5a+6>0$

$\frac{-b}{2a}<3⇒a<3$

Solving $a\in \left(-\infty ,2\right)$

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