G Tewani Solutions for Chapter: Theory of Equations, Exercise 5: DPP

The values of $a$ for which the roots of the equation $\left(a+1\right)x^2-3ax+4a=0$, $(a\ne -1)$ are real and greater than $1$ are

The equation $a{x}^4-2x^2-(a-1)=0$ will have real and unequal roots if

If $a{x}^2+bx+c=0$, $a\ne 0$, $a$, $b$, $c\in R$ has distinct real roots in $(1, 2)$, then $a$ and $5a+2b+c$ have

If $c<a<b<d$, then the roots of the equation $b{x}^2+\left(1-b\left(c+d\right)\right)x+bcd-a=0$ are

If $2a$, $b$, $2c$ are in $\text{A.P.}$, where $a$, $b$ and $c$ are $R^{+}$, then the expression $f\left(x\right)=\left(a{x}^2-bx+c\right)$ has

If $a$, $b$ and $c$ are positive numbers, such that $a>b>c$, and the equation $(a+b-2c)x^2+(b+c-2a)x+(c+a-2b)=0$ has a root in the interval $(-1$, $0)$, then

If the quadratic equation $x^2-36x+\lambda =0$ has roots $\alpha$ and $\beta$, such that $\alpha$, $\beta \in N$ and $\frac{\lambda }{5}\notin Z$ and $\lambda$ assumes the minimum possible value, then $\frac{\sqrt{\alpha +2}\sqrt{\beta +2}}{|\alpha -\beta |}$ is equal to

If the equation $2^{2x}+a·2^{x+1}+a+1=0$ has roots of the opposite sign, then the exhaustive set of real values of $a$ is