SOLUTION: c) Calculate the value of if the difference between the roots of x^2-6x+k=0 is 3.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: c) Calculate the value of if the difference between the roots of x^2-6x+k=0 is 3.       Log On


   

Question 585018: c) Calculate the value of if the difference between the roots of x^2-6x+k=0
is 3.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
p-q = 3

(x-p)(x-q)

x^2-xp-xq+pq

x^2-(p+q)x+pq


-(p+q)=-6

p+q=6
p-q=3


2p=9
p = 9/2

p+q = 6

9/2+q = 6

q = 6-9/2

q = 3/2


-----------------------

(x-p)(x-q)

x^2-xp-xq+pq

x^2-(p+q)x+pq

x^2-(9/2+3/2)x+(9/2)(3/2)

x^2-6x+27/4


So the value of 'k' is k=27%2F4