The difference between the roots of the equation 2x^2−5x+c=0 is .25. Find c.

Question

PLease help me!

Answer 1

Consider the factors to be:

(2x + r + 0.25)(x - r) = 0

-2r + r + 0.25 = -5    sum of inner and outer products equal middle term

-r = -5.25

r = 5.25

(2x + 5.25 + 0.25)(x - 5.25) = 0 

(2x + 5.5)(x - 5.25) = 0

(5.5)(-5.25) = -28.875

 

Answer 2

By the quadratic formula, x = (5 ± √(25-8c))/4

 

Since the difference of the roots is 1/4, we have:

 

    (5+√(25-8c))/4 - (5-√(25-8c))/4 = 1/4

 

      So, 2√(25-8c) = 1

 

            4(25-8c) = 1

 

            100 - 32c = 1

 

                     32c = 99

 

                         c = 99/32