Quadratic EquationHard
Question
If both roots of the equation $x^{2} - 2(a - 1)x + 2a + 1 = 0$ are positive, then
Options
A.$a < 2$
B.$a \geq 4$
C.$1 \leq a \leq 4$
D.$1 < a < 2$
Solution
$D \geq 0 \Rightarrow a \in ( - \infty,0\rbrack \cup \lbrack 4,\infty)$
$$\begin{matrix} \frac{b}{2a} > 0 \Rightarrow a - 1 > 0 \Rightarrow a \in (1,\infty) \\ f(0) > 0 \Rightarrow 2a + 1 > 0 \Rightarrow a \in \left( - \frac{1}{2},\infty \right) \end{matrix}$$
Hence, $a \in \lbrack 4,\infty)$
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