



 
Hi Claire, Well, I disagree with both your answers. You have an error in the last step.
and hence the roots are 2 and 1. Also you are looking for values of k so that the expression is never negative so it could be positive or zero and hence you want values of k so that the discriminant is ≤ 0, that is
The solution is
But this can't be correct! If k is negative then y = k(x^{2}+2x+3)  4x  2 = kx^{2}+x(2k4)+3k2 is a parabola that opens downward and hence there must be values of x where y is negative. k must be positive! so the correct answer is k ≥ 1. k ≤ 2 are the values of k for which k(x^2+2x+3)  4x  2 is never positive. I hope this helps,  


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