Question

The values of $a$ for which the equation $3x^2+2(a^2-3a+2)=0$ will have roots of opposite sign lie in the interval

• A. $(-\infty ,1)$
• B. $(-\infty ,0)$
• C. $(1,2)$
• D. $(\frac{3}{2},2)$

Answer 1

Answer: (C)

$(1,2)$

$3x^2+2(a^2-3a+2)=0$ have roots of opposite sign.
i.e. Product of roots $\alpha \beta <0$
$\Rightarrow \frac{2}{3}(a^2-3a+2)<0$
$\Rightarrow a^2-3a+2=(a-1)(a-2)<0$
$\therefore a\in (1,2)$
Hence, option C.