Question

answer the above questions with complete steps........ ​

Answer 1

Step-by-step explanation:

Given equation is

${x}^{2} - (a + 3)x - a = 0$

Since, at least one root is positive, so its discriminant will be ≥ 0

$( - (a + 3))^{2} - 4(1)( - a) \geqslant 0$

$= > (a + 3)^{2} + 4a \geqslant 0$

$= > {a}^{2} + 6a + 9 + 4a \geqslant 0$

$= > {a}^{2} + 10a + 9 \geqslant 0$

$= > {a}^{2} + 9a + a + 9 \geqslant 0$

$= > (a + 9)(a + 1) \geqslant 0$

$= > a \in [ - \infty \: \: to \: \: - 9] \: \: or \: \: a \in[ - 1 \: \: to \: \: \infty ]$