Question

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

Answer 1

Answer: 8.00

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