First slide

Theory of equations

Question

The roots of $x^{2} + a^{2} = 8 x + 6 a$ are real, then $a \in$

Easy

A

[2, 9]
B

[–2, 8]
C

[0, 7]
D

[6, 8]

Solution

$Δ \geq 0 \Rightarrow b^{2} - 4 a c \geq 0$
            $\Rightarrow 64 - 4 (a^{2} - 6 a) \geq 0$

           $\Rightarrow a^{2} - 6 a - 16 \leq 0$

           $\Rightarrow (a + 2) (a - 8) \leq 0$

           $\Rightarrow a \in [- 2, 8]$

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