List of top Mathematics Questions on Quadratic Equations

If $\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+2\hat{\mathrm{j}}-3\hat{\mathrm{k}}$, $\overrightarrow{\mathrm{b}}=3\hat{\mathrm{i}}-\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ then the angle between $\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}},\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}$ is:

If p + q + r = a + b + c = 0, then the determinant $\mathrm{\Delta }=\left|\begin{array}{lll}pa& qb& rc\\ qc& ra& pb\\ rb& pc& qa\end{array}\right|$ equals

If $\overrightarrow{a}=\hat{i}+2\hat{j}+3\hat{k}$ and $\overrightarrow{b}=\hat{i}\times (\overrightarrow{a}\times \hat{i})+\hat{j}\times (\overrightarrow{a}\times \hat{j})+\overrightarrow{k}\times (\overrightarrow{a}\times \hat{k})$ then length of $\overrightarrow{b}$ isequal to

The locus of the centre of a circle which passes through two variable points (a, 0), (–a, 0) is 

Solve for $y : 2y^{2}+6y+\frac{17}{2}=0$.

The roots of the equation $\begin{vmatrix}0&x&16\\ x&5&7\\ 0&9&x\end{vmatrix} = 0 $ are :

The general solution of the differential equation ${\log }_e\left(\frac{dy}{dx}\right)=x+y$ is

The roots $\alpha$ and $\beta$ of the quadratic equation $px^2 + qx + r = 0$ are real and opposite signs. The roots of $\alpha(x - \beta^2)+ \beta (x - \alpha)^2 = 0$ are

The roots of the equation $(3 -x)^4 + (2-x)^4$ = $(5 - 2x)^4$ are

The equations $x^2 - ax + b = 0$ and $x^2 + bx - a = 0$ have a common root, then