Q) Find the value of 'p' for which one root of the quadratic equation px2 - 14x + 8 = 0 is 6 times the other.

Let one the roots be $\alpha$ then by the given condition, other root is 6$\alpha$ We know that sum of roots (α + β) = $\frac{-b}{a}$ $\therefore$ Sum of roots α + 6α = $\frac{-(-14)}{p}$ or α = $\frac{2}{p}$ Next, we know that the product of the roots (α x β) = $\frac{c}{a}$ $\therefore$ α . 6α = $\frac{8}{p}$ or 6 $(\frac{2}{p})^2 = \frac{8}{p}$ or 6 $(\frac{4}{p^2}) = \frac{8}{p}$ or p = 3