Question

Question Find all the real zeros of g(x)=x^(3)-28x-48.

Answer 1

The real zeros of
`g(x)=x^(3)-28x-48` are x = 4, x = -3, and x = 2.

Explanation:

To find the real zeros of the cubic function
`g(x)=x^(3)-28x-48`, we employ the factorization method. Setting g(x) equal to zero, we factor the cubic expression into (x-4)(x+3)(x-2) through synthetic or polynomial division or by employing rational root theorem.

Applying the zero-product property, which asserts that if the product of several factors is zero, then at least one of the factors must be zero, we equate each factor to zero and solve for x. This yields the real zeros x = 4, x = -3, and x = 2. The factorization reflects the roots of the equation, and in this case, the roots are the values of x that make g(x) equal to zero.

Each factor corresponds to a potential solution, and by setting each factor to zero, we isolate the individual values of x that satisfy the equation. The significance of these roots lies in their ability to nullify the cubic expression, providing crucial points on the curve where the function intersects the x-axis.