SOLUTION: Let K be a real number, and consider the quadratic equation (k+1)x^2+4kx+2=0 a. Show that the discriminant of (k+1)x^2+4kx+2=0 defines a quadratic formula of k. b. Find the zeros

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Let K be a real number, and consider the quadratic equation (k+1)x^2+4kx+2=0 a. Show that the discriminant of (k+1)x^2+4kx+2=0 defines a quadratic formula of k. b. Find the zeros      Log On


   

Question 1022596: Let K be a real number, and consider the quadratic equation (k+1)x^2+4kx+2=0
a. Show that the discriminant of (k+1)x^2+4kx+2=0 defines a quadratic formula of k.
b. Find the zeros of the function in part (a), and make a sketch of its graph (NOTE: this is optional, I can do this by myself.)
c. For what value of k are there two distinct real solutions to the original quadratic equation?
d. For what value of k are there two complex solutions to the given quadratic equation?
e. For what value of k is there only one solution to the given quadratic equation?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
For the function above, a = k+1, b = 4k, and c = 2
a. The discriminant is b%5E2+-+4ac+=+%284k%29%5E2+-+4%28k%2B1%292+=+16k%5E2+-+8k+-+8
c. There will be two distinct real roots if 16k%5E2+-+8k+-+8+%3E+0. Solving this inequality gives a solution of (-infinity,-1/2)u(1,infinity).
d. There will be two complex roots (conjugates of each other) if 16k%5E2+-+8k+-+8+%3C+0. The solution will be the open interval (-1/2, 1).
e. There will be a unique solution if the discriminant is EQUAL to zero. Hence k = -1/2 or 1.