Question

Write down the polynomial that has the following:

A degree of 2, constant of 3, linear coefficient of - 2, and leading coefficient of 12.

Answer 1

The polynomial with a degree of 2, a leading coefficient of 12, a linear coefficient of -2, and a constant of 3 is 12x² - 2x + 3 = 0.

Step-by-step explanation:

The student is asking for a polynomial with specific coefficients and degree. To write down this polynomial, we need to arrange the terms with the given coefficients and constant into the standard form of a quadratic equation, which is ax² + bx + c = 0. Here, the leading coefficient a is 12, the linear coefficient b is -2, and the constant c is 3.

The resulting polynomial with the given conditions would be: 12x² - 2x + 3 = 0.

This quadratic polynomial has a degree of 2, satisfying the requirement. Remember that the degree of a polynomial is determined by the highest power of the variable x that appears in the equation.