Find the roots of the equation $\sqrt{3y+1} = \sqrt{y-1}$.

If $a+b+c=0,$ then find the value of $\frac{a^{4}+b^{4}+c^{4}}{b^{2} c^{2}+c^{2} a^{2}+a^{2} b^{2}}.$

Quantity $I$: Overall profit percentage if the cost prices of two shirts are equal. One shirt is sold for $20 \%$ profit and the other is sold for $10 \%$ loss.
Quantity $II$: Profit percentage made in selling each meter if the profit made in selling $20 \, m$ of a cloth equals the cost price of $5 \, m$ of that cloth.

If ${x^2} + px + q = 0$ is the quadratic equation whose roots are $a - 2$ and $b - 2$,where $a$ and $b$ are the roots of ${x^2} - 3x + 1 = 0$,then

The least integer $k$ which makes the roots of the equation ${x^2} + 5x + k = 0$ imaginary is

The sum of the roots of the equation,${x^2} + |2x - 3| - 4 = 0$,is