There are 2 ways to solve this question.

The first is covered by another person in the comments which is just equating the quadratic equation of the 2 roots and finding p.

The second solution, in my opinion, is much more elegant and simple and requires less complex algebraic manipulation. This method works by setting our original equation to equal what itâs roots would be ie:

3x^2 -5x +p = 3(x... more

The roots of a quadratic equation can be found with the quadratic formula: x = (-b Â± sqrt(b^2-4ac) )/2a

Putting our values of a, b and c into this formula we get x = (5Â±sqrt(25-12p)) / 6

Since one root is 3 times the other, we can set up the following equation:

(5+sqrt(25-12p))/6 = 3*(5-sqrt(25-12p))/6

Solving this equation gives p = 25/16

To check, we can put this value of p back into our so... more

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