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 then by the given condition, other root is 6

We know that sum of roots (α + β) = 

   Sum of roots α + 6α = 

or α =

Next, we know that the product of the roots (α x β) =

  α . 6α =

or 6

or 6

or p = 3