Mathematics - Quadratic Equation Question with Solution | TestHub

For $t>-1$, let ${\alpha }_t$ and ${\beta }_t$ be the roots of the equation $\left((t+2{)}^{\frac{1}{7}}-1\right)x^2+\left((t+2{)}^{\frac{1}{6}}-1\right)$ $x+\left((t+2{)}^{\frac{1}{21}}-1\right)=0$
If $$\underset{t\to -1^{+}}{\lim }{\alpha }_t=a$$ and $$\underset{t\to -1^{+}}{\lim }{\beta }_t=b$$, then $72(a+b{)}^2$ is equal to ________.