Find the value of 'p' for which one root of the quadratic equation px2

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

Ans:

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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