Question

Find the value of $\lambda$ for which the quadratic equation $3x^2+2({\lambda }^2+1)x+({\lambda }^2-3\lambda +2)=0$ has roots of opposite signs

• A. $1<\lambda <2$
• B. $1<\lambda <7$
• C. $1<\lambda <8$
• D. None of these

Answer 1

Answer: (A)

$1<\lambda <2$

As roots of opp-sign

$\Rightarrow \alpha \beta <0$ ($\alpha ,\beta$ are roots )

$\Rightarrow \frac{c}{a}<0$

$\Rightarrow \frac{({\lambda }^2-3\lambda +2)}{3}<0$

$\Rightarrow (\lambda -1)(\lambda -2)<0$

${\lambda }^2-3\lambda -2>0$

(Refer image)

$\Rightarrow 1<\lambda <2$

($\because (\lambda -1)and(\lambda -2)$ has odd Power $\therefore$ sign change at $1,2$)