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

Question

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

Professor PC Thomas Classes · Answer

(8) : Since, the given equation\ $2 x^{2}+(a-10) x+\frac{33}{2}=2 a$ has real roots.\ $	herefore \quad D \geq 0$\ $\Rightarrow(a-10)^{2}-4(2)\left(\frac{33}{2}-2 aight) \geq 0$\ $\Rightarrow \quad a^{2}+100-20 a-132+16 a \geq 0$\ $\Rightarrow \quad a^{2}-4 a-32 \geq 0$\ $\Rightarrow \quad(a-8)(a+4) \geq 0$\ $\Rightarrow a \in(-\infty,-4] \cup[8, \infty)$\