Question

Consider this polynomial equation.

6(x3)(x² + 4) (x + 1) = 0
Use the equation to complete this statement.
The equation has
solutions. Its real solutions are

Answer 1

To find the polynomial’s solutions, we need to factor it and apply the zero product property.

*I am going to assume that (x3) is actually x^3*

6(x^3)((x^2+4)(x+1)=0

According to the zero product property,
if a•b=0, then a=0 or b=0. So, we can take each term and set it equal to zero.

x^3=0

(Cube root) of x^3 = (cube root) of 0

x=0

(x^2+4)=0

x^2=-4

x= +/- i•2 (Not a real solution; it’s complex)

x+1=0

x=-1


So, x=-1, 0