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

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) (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
c. There will be two distinct real roots if . Solving this inequality gives a solution of (,-1/2)u(1,).
d. There will be two complex roots (conjugates of each other) if . 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.
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