Question

The least positive value of '$a$' for which the equation, $2x^2+(a-10)x+\frac{33}{2}=2a$ has real roots is

Answer 1

$2x^2+(a-10)x+\frac{33}{2}=2a$ has real roots.
$\Rightarrow D\ge 0$

$\Rightarrow (a-10{)}^2-4\times 2\times (\frac{33}{2}-2a)\ge 0$
$\Rightarrow (a-10{)}^2-4(33-4a)\ge 0$
$\Rightarrow a^2-4a-32\ge 0$
$\Rightarrow a\in (-\infty ,-4]\cup [8,\infty )$

Thus, the least positive value of '$a$' is $8$.