First slide

Theory of equations

Question

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

Moderate

Solution

$\begin{array}{l} D \geq 0 \\ (a - 10)^{2} - 4 (2) (\frac{33}{2} - 2 a) \geq 0 \\ (a - 10)^{2} - 4 (33 - 4 a) \geq 0 \\ a^{2} - 4 a - 32 \geq 0 \Rightarrow a \in (- \infty, - 4] \cup [8, \infty) \end{array}$

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