Question

Find the set of values of ${}^{\prime }{a}^{\prime }$ if the points $(1,2)$ and $(3,4)$ lie to the same side of the straight line $3x-5y+a=0$

Answer 1

Putting (1,2) and (3,4) should give a result with the same sign $\Rightarrow$ Product of them would be positive

$\Rightarrow (3-10+a)(9-20+a)\ge 0$

$\Rightarrow (a-7)(a-11)\ge 0$

$a\in (-\infty ,7]\cup [11,\infty )$