First slide

Theory of expressions

Question

One lies between the roots of the equation $- x^{2} + ax + a = 0, a \in R$ if and only if a lies in the interval

Moderate

A

$(\frac{1}{2}, \infty)$
B

$[- \frac{1}{2}, \infty)$
C

$(- \infty, \frac{1}{2})$
D

$(- \infty, \frac{1}{2}]$

Solution

$\begin{array}{l} - x + ax + a = 0 \\ \Rightarrow x^{2} - ax - a = 0 \\ Let f (x) = x^{2} - ax - a \\ f (1) < 0 \\ \Rightarrow 1 - a - a < 0 \\ \Rightarrow 1 < 2 a \\ \Rightarrow a > \frac{1}{2} \end{array}$

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