Option: C is the correct answer.
C.) x = −3.8, 3
The function f(x) is given by:
[tex]f(x)=x^2-x-12[/tex]
and the function g(x) is given by:
[tex]g(x)=-1.8x-0.6[/tex]
Now, we are asked to find the solution of the equation:
[tex]f(x)=g(x)[/tex]
i.e. we have to find the value of x such that both the functions are equal i.e.
[tex]x^2-x-12=-1.8x-0.6\\\\i.e.\\\\x^2-x+1.8x-12+0.6=0\\\\i.e.\\\\x^2+0.8x-11.4=0\\\\i.e.\\\\10x^2+8x-114=0\\\\i.e.\\\\5x^2+4x-57=0[/tex]
Now, on solving the equation using the quadratic formula i.e. the solution of the equation:
[tex]ax^2+bx+c=0[/tex]
is given by:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here we have:
[tex]a=5,\ b=4\ and\ c=-57[/tex]
Hence, the solution is given by:
[tex]x=\dfrac{-4\pm \sqrt{4^2-4\times 5\times (-57)}}{2\times 5}\\\\i.e.\\\\x=\dfrac{-4\pm \sqrt{16+1140}}{10}\\\\i.e.\\\\x=-3.8\ and\ x=3[/tex]
