SOLUTION: Find the value of p if the roots of the quadratic equation 4x^2-(5p+1)x+5p=0 differ by 1
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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) (Show Source): You can put this solution on YOUR website!
Note that the roots of the quadratic are in the form
 \pm \sqrt{(5p+1)^2 - 4(4)(5p)}}{8} = \frac{-5p - 1}{8} \pm \frac{\sqrt{25p^2 - 70p + 1}}{8})
(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 - 3) = 0)
p = -1/5 or p = 3.
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