Question

What are the roots of the polynomial equation x^4+x^3=4x^2+4x? Use a graphing calculator and a system of equations.

Answer 1

Desmos graphing calculator will draw this graph for you.

draw 2 curves

y = x^4 + x^3 
and
y = 4x^2 + 4x

The roots are the points where the 2 curves intersect.

You can see by simple substitution that one root is zero.

x^4 + x^3 - 4x^2 - 4x = 0

f(2)  = 16 + 8 - 4(4) - 4(2)  = 0   so 2 is another root

f(-2) = 16 - 8 - 16 + 8 = 0  so  -2 is another root

f(-1) = 1 - 1  - 4 + 4 = 0 so -1 is the other root

The answer is A

Answer 2

 the answer is a i hope that helpful