SOLUTION: Find the value of p if the roots of the quadratic equation 4x^2-(5p+1)x+5p=0 differ by 1

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find the value of p if the roots of the quadratic equation 4x^2-(5p+1)x+5p=0 differ by 1      Log On


   

Question 463055: Find the value of p if the roots of the quadratic equation 4x^2-(5p+1)x+5p=0 differ by 1
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Note that the roots of the quadratic are in the form

(upon simplification). If we want these roots to differ by 1, we need to set the equality



This is so that the roots will be in the form k + (1/2) and k - (1/2), differing by 1. Solving this equation for p,





Luckily, this factors:



p = -1/5 or p = 3.