Answer:
Descarte's rule says that the polynomial will have the number of zeroes equal to the number of times the sign off the coefficient changes.
For positive real roots:

The coefficient of polynomial is:
+9 -4 +10
There is 2 time sign in changing in 1st and 2nd term and then in 2nd and 3rd term.
So,there will be 2 positive real roots or less but even.
For negative real roots find P(-x)


So, coefficient of above polynomial is:
-9 +4 -10
There is 2 time sign in changing in 1st and 2nd term and then in 2nd and 3rd term.
So,there will be 2 negative real roots or less but even.
System:
y ≤ -x + 4
y >

x
Notes:
1. inequalities are expressed in slope-intercept form. y = mx + b
2. the second inequality uses the greater than inequality symbol rather than the greater or equal to symbol due to the broken line.
3. All points in the shaded region will satisfy both inequalities. Point outside the shaded region will not satisfy both inequalities.
Just add up the two functions
(f+g)(x)=(7x^3-2x-12)+(-3x^3-8x^2+10x)
(f+g)(x)=4x^3-8x^2+8x-12
unfortunately you choice isn't correct. it's the fourth choice