Question

The value of a for which the quadratic equation $3x^2+2(a^2+1)x+(a^2-3a+2)=0$ possesses real roots of the opposite sign lies in

• A.
• B. (1, 2)
• C. (3/2, 2)
• D. [1, 2]

Answer 1

The correct option is B (1, 2)

To have 2 roots of the opposite sign, the product of the roots need to be negative and the equation should have real roots

$4(a^2+1{)}^2-12(a^2-3a+2)\ge 0$ and $\frac{(a^2-3a+2)}{3}<0$ i.e., $(a-1)(a-2)<0$ or $1<a<2$