G Tewani Solutions for Chapter: Theory of Equations, Exercise 2: DPP

If $a, b, c\in R$ and $3b^2-8ac<0,$ then the equation ${\mathrm{ax}}^4+$ $b{x}^3+c{x}^2+5x-7=0$ has

For real solution of equation $\sqrt[3]{x+3p+1}-\sqrt[3]{x}=1,$ we have

For $a, b, c$ non-zero, real and distinct, the equation, $\left(a^2+b^2\right)x^2$ $-2b(a+c)x+b^2+c^2=0$ has non-zero real roots. One of these roots is also the root of the equation

The equation $x^2+bx+c=0$ has distinct roots. If $2$ is subtracted from each root, the result are the reciprocal of the original roots, then $b^2+c^2$ is

The equation ${\left(x^2+3x+4\right)}^2+3\left(x^2+3x+4\right)+4=x$ has

If $c\ne 0$ and the equation $\frac{p}{2x}=\frac{a}{x+c}+\frac{b}{x-c}$ has two equal roots, then $p$ can be

The equation $(ay-bx{)}^2+4xy=0$ has rational solutions $x, y$ for

Let $a, b, c$ and $m\in R^{+},$ the possible value of $m$ (independent of $a, b$ and $c$) for which at least one of the following equations have real roots, is

$a{x}^2+bx+cm=0$, $b{x}^2+cx+am=0$, $c{x}^2+ax+bm=0$.