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  4. The least positive value of 'a' for which the equation, 2x2+(a-10)x + (33/2) = 2a has real roots is . Given --

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Q. 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 --

JEE MainJEE Main 2020Complex Numbers and Quadratic Equations

Solution:

$D\ge0 \Rightarrow \left(a-10\right)^{2}-4\times2\times\left(\frac{33}{2}-2a\right)\ge0$
$\Rightarrow a^{2}-4a+-32\ge0$
$\Rightarrow a\,(\in -\infty, 4] \cup [8, \infty)$