SOLUTION: Find the value of k for the equal equation (k+4) x+(k+1) x+1=0has equal roots

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Question 928877: Find the value of k for the equal equation (k+4) x+(k+1) x+1=0has equal roots
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
I guess you have quadratic equation:

%28k%2B4%29x%5E2%2B%28k%2B1%29x%2B1=0
in the quadratic equation ax%5E2+%2Bbx+%2Bc=0 the roots are equal when
the discriminant b%5E2-4ac+=+0
comparing the equation
a=+%28k%2B4%29
+b=+%28k%2B1%29
+c=1
so,
%28k%2B1%29%5E2-4%28k%2B4%29%281%29=0
k%5E2%2B2k%2B1-4k-16=0
k%5E2-2k-15=0
k%5E2-5k%2B3k-15=0
k%28k-5%29%2B3%28k-5%29=0
%28k-5%29%28k%2B3%29=0
k=5 or k=-3+

check the roots:
%28k%2B4%29x%5E2%2B%28k%2B1%29x%2B1=0 if k=5
%285%2B4%29x%5E2%2B%285%2B1%29x%2B1=0
9x%5E2%2B6x%2B1=0
9x%5E2%2B3x%2B3x%2B1=0
%289x%5E2%2B3x%29%2B%283x%2B1%29=0
3x%283x%2B1%29%2B%283x%2B1%29=0
%283x%2B1%29%283x%2B1%29=0...roots will be same

3x%2B1=0=>x=-1%2F3... double solution

+graph%28+600%2C+600%2C+-5%2C+5%2C+-5%2C+10%2C+%283x%2B1%29%283x%2B1%29%29+