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(C) The given equation is $2x^{2} + (a-10)x + (\frac{33}{2} - 2a) = 0$.For real roots,the discriminant $D$ must be greater than or equal to $0$.$D = (

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$8$

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(C) The given equation is $2x^{2} + (a-10)x + (\frac{33}{2} - 2a) = 0$.For real roots,the discriminant $D$ must be greater than or equal to $0$.$D = (a-10)^{2} - 4(2)(\frac{33}{2} - 2a) \geq 0$.$D = a^{2} - 20a + 100 - 8(\frac{33-4a}{2}) \geq 0$.$D = a^{2} - 20a + 100 - 4(33-4a) \geq 0$.$D = a^{2} - 20a + 100 - 132 + 16a \geq 0$.$D = a^{2} - 4a - 32 \geq 0$.$(a-8)(a+4) \geq 0$.This inequality holds for $a \in (-\infty, -4] \cup [8, \infty)$.Since we are looking for the least positive value of $a$,we consider the interval $[8, \infty)$.The least positive value is $8$.

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

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