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?

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)   (Show Source): You can put this solution on YOUR website!

You are given an equation

= .

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 :

           + = = .

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

          . = .

Now, the condition of the problem requires that

+ = .,

which implies that

= .

Hence, p = = .

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!

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