Solve the given two equations and select the correct option.
$I. 15x^2 - 46x + 35 = 0$
$II. 4y^2 - 15y + 14 = 0$

All the values of $m$ for which both roots of the equation $x^2 - 2mx + m^2 - 1 = 0$ are greater than $-2$ but less than $4$ lie in the interval

In a cubic equation,the coefficient of $x^2$ is zero and the remaining coefficients are real. If one root is $\alpha = 3 + 4i$ and the remaining roots are $\beta$ and $\gamma$,then find the value of $\alpha \beta \gamma$.

Solve the given two equations and select the correct answer from the given options.
$I. 2x^2 + 3x + 1 = 0$
$II. 12y^2 + 7y + 1 = 0$

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2}-11x+24=0$
$II.$ $2y^{2}-9y+9=0$

If the roots of the equation ${x^2} - 8x + ({a^2} - 6a) = 0$ are real,then