List of top Mathematics Questions on Quadratic Equations asked in MHT CET

The value of 'a' so that the sum of squares of the roots of the equation $x^2 - (a - 2)x - a + 1 = 0$ assumes the least value is

The value of 'a' so that the sum of squares of the roots of the equation $x^2 - (a - 2)x - a + 1 = 0$ assumes the least value is

Find the roots of the quadratic equation \( x^2 - 5x + 6 = 0 \).

Consider the following statements:1. If $y=\ln (\sec x+\tan x)$, then $\frac{dy}{dx}=\sec x$.2. If $y=\ln (\mathrm{cosec}x-\cot x)$, then $\frac{dy}{dx}=\mathrm{cosec}x$.Which of the above is / are correct?

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:

The point which does not belong to the feasible region of the LPP:Minimize: $\mathrm{Z}=60\mathrm{x}+10\mathrm{y}$subject to $3\mathrm{x}+\mathrm{y}\ge 18$$2x+2y\ge 12$$x+2y\ge 10$$\mathrm{x},\mathrm{y}\ge 0$ is:

If ${\cos }^{-1}\left(\frac{p}{a}\right)+{\cos }^{-1}\left(\frac{q}{b}\right)=\alpha$, then $\frac{p^2}{a^2}+k\cos \alpha +\frac{q^2}{b^2}={\sin }^2\alpha$ where $\mathrm{k}$ is equal to:

Find the position vector of the midpoint of the vector joining the points $P(2,3,4)$ and $Q(4,1,-2)$.