First slide

Theory of equations

Question

$If the equation x^{2} + 2 | a | x + 4 = 0 has integral roots, then minimum value of a is$

Moderate

A

4
B

$- \frac{5}{2}$
C

0
D

$- 4$

Solution

$Let α, β be the roots of the given equation.$
$\begin{array}{l} Clearly α, β < 0 \\ \Rightarrow α + β = - 2 | a | and α β = 4 \end{array}$
$Since α, β < 0 a n d p r o d u c t i s 4 possible values of (α, β) are (- 1, - 4) and (- 2, - 2)$
$\begin{array}{l} \Rightarrow - 2 | a | = - 5 or - 2 | a | = - 4 \\ |a| = \frac{5}{2} o r |a| = 2 \\ a = \pm \frac{5}{2} o r \pm 2 \\ Hence, the minimum value of a is - \frac{5}{2} \end{array}$

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