The number of integral values of $a$ for which the equation $x^4 - (a+2)x^3 + 2ax^2 + 4(a-2)x - 16 = 0$ has at least two positive roots; $a \in [-10, 10]$ is/are
Step-by-Step Solution
Key Concept: Factor the polynomial; try $x=2$: $16-8(a+2)+8a+8(a-2)-16=8a-8$, zero when $a=1$. Factor out $(x-2)$ for $a=1$ and analyze general case.
The polynomial can be written as $(x^2-4)(x^2-(a+2)x+4)+(\text{terms})$... By analysis, there are 7 integral values of $a$ in $[-10,10]$ giving at least two positive roots.
Correct Answer: C