SOLUTION: Kx^2+kx+5=0 what is the value of "k"

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Kx^2+kx+5=0 what is the value of "k"      Log On


   

Question 697245: Kx^2+kx+5=0 what is the value of "k"
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
kx%5E2%2Bkx%2B5=0+
If the discriminant b%5E2+-+4ac+=+0, then the solution will have equal roots or only one solution

here b+=+k
a+=+k
c+=+5
so
k%5E2+-+4%2Ak%2A5+=+0
k%5E2+-+20k+=+0
k%28k+-+20%29+=+0...since k%3C%3E0 product will be equal to zero if
k+-+20=0
so
k+=20

then you have:
20x%5E2%2B20x%2B5=0+

check if the roots are equal:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-20+%2B-+sqrt%2820%5E2-4%2A20%2A5+%29%29%2F%282%2A20%29+
x+=+%28-20+%2B-+sqrt%28400-400+%29%29%2F40+
x+=+%28-20+%2B-+sqrt%280%29%29%2F40+
x+=+%28-20+%2B-+0%29%2F40+
x+=+-20%2F40+
x+=+-1%2F2+.......so, we have only one root

see it on a graph:

+graph%28+600%2C+600%2C+-5%2C+5%2C+-5%2C+5%2C+20x%5E2%2B20x%2B5%29+