Plz Help anybody

The roots are 3 and -k

so the base length  is  |3 - - k| = |3+K|

The height is given by the y intercept  which is |0.5 * -3 * k| = | -1.5k |

\(A=0.5*|3+k|*|-1.5k|\\ A=0.5*1.5*|k|*|3+k|\\ \text{but we want this to equal } 1.5\\ 1.5=0.5*1.5*|k|*|3+k|\\ 1=0.5*|k|*|3+k|\\ 2=|k|*|3+k|\\~\\ If\;\;k<-3\;\;then\\ 2=-k*-(3+k)\\ 2=+k(3+k)\\ ...\\ k=\frac{-3\pm\sqrt{17}}{2}\\ k=k=\frac{-3-\sqrt{17}}{2}\\ k\approx -3.56\)

\(If\;\;-3

\(If\;\;k>0\;\;then\\ 2=k*(3+k)\\ ...\\ k=\frac{-3\pm\sqrt{17}}{2}\\ k=\frac{-3+\sqrt{17}}{2}\\ k\approx 0.56\)

So       \(\boxed{k=-2,\;-1, \; \frac{-3-\sqrt{17}}{2},\; \frac{-3+\sqrt{17}}{2}\\ \text{would all work}}\)

It would be a good idea to test each of these for validity.

LaTex:

A=0.5*|3+k|*|-1.5k|\\
A=0.5*1.5*|k|*|3+k|\\
\text{but we want this to equal } 1.5\\
1.5=0.5*1.5*|k|*|3+k|\\
1=0.5*|k|*|3+k|\\
2=|k|*|3+k|\\~\\
If\;\;k<-3\;\;then\\
2=-k*-(3+k)\\
2=+k(3+k)\\
...\\
k=\frac{-3\pm\sqrt{17}}{2}\\
k=k=\frac{-3-\sqrt{17}}{2}\\
k\approx -3.56

If\;\;-3 2=-k*(3+k)\\
-2=k(3+k)\\
...\\
k=\frac{-3\pm\sqrt{17}}{2}\\
k=\frac{-3+\sqrt{17}}{2}\\
k\approx 0.56

I did it graphically and got one answer of   k=0.56    (probably correct to 2 decimal places)

Thanks Melody! 

Some of my LaTex, (therefore some of my answer) has disappeared