[SOLVED] High School Quadratic Inequalities

Q) Use the discriminant 'b^2=-4ac' to solve the following:

i) Find the values of ' k ' for which the following equations have two separate roots.

a) $\displaystyle kx^2+kx+2=0$

**Answer is 0>k>8**

I solved the above to get

$\displaystyle k(k-8)>0$

Now my question is that we know that k>8 but how do we figure k<0?

Is it because we are 100% that if k>8 from my final step then the other value must be smaller? (k<0)

ii) Find the values of ' k ' for which the following equations have no roots.

a) $\displaystyle k^2x^2+2kx+1=0$

I solved this and got:

$\displaystyle 4k^2-4k^2<0$

$\displaystyle 0<0$

**Answer is k=0**

How is the answer k=0? I mean shouldn't 0<0 mean no solution or something?

iii) Sketch, on the same diagram, the graphs of $\displaystyle y=1/x$ and $\displaystyle y=x-3/2$. Find the solution set of the inequality $\displaystyle x-3/2>1/x$

Please tell me step by step on how to solve this question.

Thanks in advance!