Answer:
k=4
[tex]5x^2-x-4=0[/tex]
Step-by-step explanation:
To solve this example we use Viet's rule. So if we have equation:
[tex]ax^2+bx+c=0[/tex], then we use Viet :
[tex]x_{1} +x_{2}=\frac{-b}{a} \\x_{1}*x_{2}=\frac{c}{a}[/tex]
Now, by question we have this :
[tex]x_{1}+x_{2}=\frac{1}{5}=0.2\\ x_{1}*x_{2}=-\frac{k}{5} \\\\x_{1}-x_{2}=1.8[/tex]
From the last we have :
[tex]x_{1}=1.8+x_{2} \\[/tex]
Now use first equation :
[tex]1.8+x_{2}+x_{2}=0,2\\x_{2}=-0.8[/tex]
Now, we can find x1=1
Now, we can find k :
[tex]1*(-0.8)=-\frac{k}{5} \\k=4[/tex]
