Quadratic Equations - Algebra - Mathematics Previous Year Questions

If $A=\left\{x \in R / x^2+5|x|+6=0\right\}$ then $n(A)=\ldots \ldots$

The rational form of a number 1.$\overline{41}$ is

The quadratic equation whose roots are the numbers having arithmetic mean 34 and geometric mean 16 is

The equation \(x^3+x-1=0\) has

The equation $\mathrm{e}^{\sin x}-\mathrm{e}^{-\sin x}=4$ has ̱_________ solutions.

The equation $(\operatorname{cosp}-1) x^2+(\cos p) x+\operatorname{sinp}=0$ in the variable $x$, has real roots. Then p can take any value in the interval

The equation $(\operatorname{cosp}-1) x^2+(\operatorname{cosp}) x+\sin p=0$ in the variable $x$, has real roots. Then p can take any value in the interval

Let $\alpha, \beta$ be the roots of the equation $x^2-\mathrm{p} x+\mathrm{r}=0$ and $\frac{\alpha}{2}, 2 \beta$ be the roots of the equation $x^2-q x+r=0$. Then the value of r is

If $\mathrm{f}(x)=2 x^3+\mathrm{m} x^2-13 x+\mathrm{n}$ and 2,3 are the roots of the equation $\mathrm{f}(x)=0$ then the value of $4 m+5 n$ is