SOLUTION: Please help me solve this polynomial equation. Find 'K' so that 9x^2+kx+4=0 has exactly one root.

Question 107434: Please help me solve this polynomial equation.
Find 'K' so that 9x^2+kx+4=0 has exactly one root.
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
9x^2+kx+4=0
Let k=b to avoid later confusion with a different k in another formula later in the problem
9x^2+bx+4=0
An quadratic equation has one root when its vertex is the root.
Vertex=(h,k). k=0 because the vertex touches the x line (k=0)
f(x)=a(x-h)^2+k Standard form of a quadratic function.
=9(x-h)^2+0
=9(x-h)^2
9h^2=4
3h=+-2 sqrt of both sides.
h=+-2/3
since the equation calls for b being positive then h= -2/3
9(x+(2/3))^2
=9(x^2+4x/3+4/9
=9x^2+12x+4
b=12 Answer
Note in the graph that there is only one answer for x at x= -2/3
Ed

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