SOLUTION: Find k such that the equation kx squared + x + 100k=0 has a repeated solution K=? Use a comma to separate answers

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Question 1122815: Find k such that the equation kx squared + x + 100k=0 has a repeated solution
K=?
Use a comma to separate answers
Found 2 solutions by solver91311, josmiceli:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


In order for a quadratic to have one zero with a multiplicity of two, the discriminant, i.e. , must equal zero.



Solve for the two possible values of


John

My calculator said it, I believe it, that settles it

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In the quadratic formula, for repeated solutions
(1) +b%5E2+-+4%2Aa%2Ac+=+0+
and
(2) +x+=+-b%2F%28+2a+%29+
——————————-
+k%2Ax%5E2+%2B+x+%2B+100k+=+0+
+b+=+1+
+a+=+k+
+c+=+100k+
(1) +1%5E2+-+4%2Ak%2A100k+=+0+
(1) +1+-+400k%5E2+=+0+
(1) +k%5E2+=+1%2F400+
+k+=+1%2F20+
or
+k+=+-1%2F20+
—————————
The equation is
+%281%2F20%29%2Ax%5E2+%2B+x+%2B+100%2A%28+1%2F20%29+
+%281%2F20%29%2Ax%5E2+%2B+x+%2B+5+=+0+
Check both solutions with quadratic equation