Quadratic Equation Part 1

How to do these?

1. Find the real roots of $\displaystyle 2x^2+3x-1=0$. Give your answer in surd form.

2. Find the range of values of q if $\displaystyle x^2+(q+1)x+q+1=0$ has complex roots.

3. Find the range of values of m if $\displaystyle x^2+x+1=m(x+2)$ has real and distinct roots.

4. Find the range of values of k if $\displaystyle x^2+(k-3)x+k=0$ has roots with same sign.

Answer:

1. $\displaystyle \frac{1}{2}(-3 \pm \sqrt{17})$

2. -1<q<3

3. $\displaystyle m<-3-2\sqrt{3},m>-3+2\sqrt{3}$

4. k>0