Given #2x^2-kx+(k-2) = 0#, is there some value of #k# such that both roots are negative?
Now, we know that, if
In our case, then, from this, it follows that,
Knowing that, both,
We conclude that,
can not have roots both negative.
Both roots cannot be negative.
The solutions of this equation is
We compare this equation to
Let's calculate the discriminant
the roots of the equation are
If the trinom has both roots negative then all its coefficients must be positive.
More briefly, given:
#2x^2-kx+(k-2) = 0#
Note that the sum of the coefficients is
#2-k+k-2 = 0#