Answer:
[tex]x = \frac{ - 13}{16} [/tex]
Step-by-step explanation:
[tex]f(x) = {x}^{3} + 3 \\ g(x) = {x}^{2} + 2[/tex]
At the point of intersection, f(x)=g(x)
[tex] {x}^{3} + 3 = {x}^{2} + 2 \\ collect \: like \: terms \\ {x}^{3} - {x}^{2} + 3 - 2 = 0 \\ {x}^{3} - {x}^{2} + 1 = 0[/tex]
[tex] {x}^{3} - {x}^{2} + 1 = 0[/tex]
The above graph is that of the equation
[tex] {x}^{3} - {x}^{2} + 1 = 0[/tex]
The solution is = -0.755 which is approximately -0.8
From the option provided;
For option A, x = -13/16 = -0.8125
For option B, x = -5/4 = -1.25
For option C, x = -15/16 = -0.9375
For option D, x = -7/8 = -0.875
From the option provided, The closest to the solution is Option A
Because - 0.8125 is approximately -0.8
