Hello! So I am taking supplementary Math classes as a prerequisite and I’m having trouble with answering different exercises (possibly because I do not have a solid foundation). Anyway, we were given this exercise problem:
“Find all real values of k such that the equation [x^2+kx+k=x-2] has exactly one solution.”
I have a gist on what to so but I don’t exactly know how to do it...
So far, what I have done is:
My teacher gave the clue that in order for the equation to have one solution, the discriminant (b^2-4ac) in the quadratic formula must equate to 0. So far, I think ‘b’ would be (k-1), ‘a’ would be 1, and ‘c’ would be (k+2). I know the only thing I probably have to do is substitute this and solve but I honestly do not understand how I’m supposed to do that nor do I know how that would look like.
I’m hoping that somebody here could show me a step by step process on how to solve this problem as a reference for future problems similar to this one. Thank you for your time!
“Find all real values of k such that the equation [x^2+kx+k=x-2] has exactly one solution.”
I have a gist on what to so but I don’t exactly know how to do it...
So far, what I have done is:
- rewrite the equation as [x^2 + x(k-1) + (k+2) = 0] so that it would be in standard form.
My teacher gave the clue that in order for the equation to have one solution, the discriminant (b^2-4ac) in the quadratic formula must equate to 0. So far, I think ‘b’ would be (k-1), ‘a’ would be 1, and ‘c’ would be (k+2). I know the only thing I probably have to do is substitute this and solve but I honestly do not understand how I’m supposed to do that nor do I know how that would look like.
I’m hoping that somebody here could show me a step by step process on how to solve this problem as a reference for future problems similar to this one. Thank you for your time!
