The least positive value of 'a' for which the equation 2x^2+(a-10)x+332=2a has real roots …

Question

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

Answer: 8

Accepted Answer

$D\ge0$: $(a-10)^2-8\left(\dfrac{33}2-2a\right)\ge0 \implies a^2-4a-32\ge0 \implies (a-8)(a+4)\ge0 \implies a\le-4$ or $a\ge8$.

Least positive value: $a=8$.

Solutions · 1