Question

kx^2 + (k+2)x -3 =0 has roots which are real and positive. Find the possible values that k may have.


I understand that I have to use the discriminant to solve this, but I can't seem to get the answer right, so I really need help!!

Answer 1

b^2=4ac
so,
(k+2)^2=-12k
k^2+4+4k=-12k
k^2+16k+4=0

Answer 2

Hello
It's a given that we have two roots.

The roots must be real and distinct at that. So the disc. has to be nonzero and positive.

The two roots must also be positive. This means that both the product and the sum of the roots ought to be positive.

Suppose (alpha) and (beta) are the two roots.I'd construct a sign diagram, k against the disc., as well as k against (alpha)*(beta) and k against (alpha)+(beta),and eventually find the values for k such that the values of the three (disc., (alpha)*(beta) and (alpha)+(beta)) are positive simultaneously.