Final answer:
To determine the polynomial in standard form, the terms must be arranged in descending powers with no missing powers. The quadratic formula can be used for solving quadratic equations. The provided options are all in standard form; the correct choice must meet the specific terms and sign requirements.
Step-by-step explanation:
To find the polynomial in standard form with the given requirements, we need to ensure that the polynomial is written with degrees in decreasing order and with no missing powers of x. To show how to do this, let's consider the quadratic equation x² +0.0211x -0.0211 = 0 which is an example of a polynomial in standard form, where the coefficients of x are in descending powers.
A general quadratic equation can be written as ax² + bx + c = 0. To solve for x, we use the quadratic formula, x = −b ± √(b² − 4ac) / (2a). For example, if we were to substitute a = 3, b = 13, and c = −10 into the quadratic formula, we would have x = −13 ± √(169 − 4 × 3 × (−10)) / (2 × 3) which simplifies to x = −13 ± √(169 + 120) / 6.
Similarly, if you are given another quadratic equation, let's say at² + bt + c = 0 with different coefficients, such as a = 4.90, b = 14.3, and c = −20.0, the process would be the same; plug the values into the quadratic formula to find the values of t.
In conclusion, the original polynomials provided are all in standard form as they list powers of x in descending order. A correct polynomial in standard form should be a single expression that corresponds to the given specification, including the order of terms and the signs of coefficients.