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

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