Which statement best describes the equation x5 + x3 – 14 = 0?
The equation is quadratic in form because it is a fifth-degree polynomial.
The equation is quadratic in form because the difference of the exponent of the lead term and the exponent of the middle term is 2.
The equation is not quadratic in form because it cannot be rewritten as a second-degree polynomial.
The equation is not quadratic in form because the exponent of the lead term is not the square of the exponent of the middle term.

Respuesta :

Answer:

2.The equation is not quadratic in form because it cannot be rewritten as a second-degree polynomial.

Step-by-step explanation:

A quadratic equation is any equation that can be rearranged in standard form as :

ax² + bx + c = 0

Where a, b and c are coefficients and a ≠ 0.

Since for a quadratic equation, the power of x is a non negative integer, it is considered as a polynomial. A quadratic equation is a second-degree polynomial (i.e the gratest power of x is two).

The equation  is not a quadratic equation because it cannot be rewritten as a second-degree polynomial.

We want to see which statement describes the equation x^5 + x^3 - 14 = 0.

The correct option is:

The equation is not quadratic in form because it cannot be rewritten as a second-degree polynomial.

First, our equation:

x^5 + x^3 - 14 = 0.

Is a polynomial of degree 5 (the degree is equal to the maximum exponent).

Thus, this is not a quadratic equation.

Where a quadratic equation is a polynomial of degree 2.

Notice that we also can't replace x by another variable, such that it becomes a quadratic equation, then the correct statement is:

The equation is not quadratic in form because it cannot be rewritten as a second-degree polynomial.

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