SOLUTION: Find the value of k so that the equation 3x²-(5+k)x-17=0 will have roots numerically equal but opposite sign.Please answer the question.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Find the value of k so that the equation 3x²-(5+k)x-17=0 will have roots numerically equal but opposite sign.Please answer the question.      Log On


   

Question 367586: Find the value of k so that the equation 3x²-(5+k)x-17=0 will have roots numerically equal but opposite sign.Please answer the question.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
For the roots to be numerically equal but opposite in signs, the factorization of the expression would have to be (ax+b)(ax-b) = a%5E2x%5E2+-+b%5E2, a difference of two squares. This means a%5E2+=+3, and b%5E2+=+17. The middle term has to disappear, and so -(5+k) = 0, or k = -5.