Answer:
The solution of the quadratic equation [tex]15g^{2}+ 17g - 110 = 0[/tex] are [tex]g = (-\frac{10}{3}, \frac{11}{5})[/tex].
Step-by-step explanation:
The quadratic equation is: [tex]15g^{2}+ 17g - 110 = 0[/tex]
Use factorization method to determine the roots of g.
Factor the equation [tex]15g^{2}+ 17g - 110 = 0[/tex] as follows:
[tex]15g^{2}+ 17g - 110 = 0\\15g^{2}+ 50g - 33g - 110 = 0\\5g (3g + 10) - 11 (3g + 10) = 0\\(5g - 11) (3g + 10) = 0[/tex]
First substitute [tex](5g - 11)[/tex] equal to 0 and solve for g as follows:
[tex](5g - 11)=0\\5g=11\\g=\frac{11}{5}[/tex]
Now, substitute [tex](3g + 10)[/tex]equal to 0 and solve for g as follows:
[tex](3g + 10)=0\\3g=-10\\g=-\frac{10}{3}[/tex]
So, the solution of the quadratic equation [tex]15g^{2}+ 17g - 110 = 0[/tex] are [tex]g = (-\frac{10}{3}, \frac{11}{5})[/tex]
