Question

1. Determine whether -3 is a root of x3 + 3x2 + x + 1 = 0.

Answer 1

Answer:

1. The given equation does not have root at x = - 3.

2. (x - 3) (x + 1) (x² + 4) = 0

This curve will intersect twice the x-axis.

Step-by-step explanation:

1. If the right hand side of the equation $x^{3} +3x^{2} +x+1 =0$  ......... (1) becomes same as the left hand side by putting x = - 3, then only we can conclude that x = - 3 is a root of the equation.

But in this case $(-3)^{3} + 3(-3)^{2}+(-3) +1 \neq 0$.

Therefore, x = - 3 is not a root of the above equation (1).

2. The equation of the polynomial with roots 3, -1, 2i, and -2i is

(x - 3) (x + 1) (x - 2i) (x + 2i) = 0

⇒ (x - 3) (x + 1) (x² + 4) = 0 (Answer)

Therefore, the graph of the above curve will intersect twice the x-axis in a real coordinate plane, at x = 3 and at x = -1. (Answer)