SOLUTION: (This problem is about the sum and product of roots of quadratic equations) For what value of p does the sum of roots of the equation 6x^2-3px+5=0 equal the product of roots?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: (This problem is about the sum and product of roots of quadratic equations) For what value of p does the sum of roots of the equation 6x^2-3px+5=0 equal the product of roots?      Log On


   

Question 979693: (This problem is about the sum and product of roots of quadratic equations)
For what value of p does the sum of roots of the equation 6x^2-3px+5=0 equal the product of roots?
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!

You are given an equation

6x%5E2-3px%2B5 = 0.

Apply the  Viete's theorem  (see the lesson  Solving quadratic equations without quadratic formula  in this site):

According to this theorem,
    a)  the sum of the roots of the quadratic equation is equal to the coefficient at  x  taken with the opposite sign and divided by the coefficient at x%5E2:

          x%5B1%5D + x%5B2%5D = 3p%2F6 = p%2F2.

    b)  the sum of the roots is equal to the constant term divided by the coefficient at x%5E2:

          x%5B1%5D.x%5B2%5D = 5%2F6.

Now,  the condition of the problem requires that

x%5B1%5D + x%5B2%5D = x%5B1%5D.x%5B2%5D,

which implies that

p%2F2 = 5%2F6.

Hence,  p = 2%2A%285%2F6%29 = 5%2F3.

As a last step,  substitute this value of  p  into the original equation,  find its roots and make sure that the roots satisfy to the imposed condition.
Please,   do it yourself.     Good luck!