Which of the following is a root of the polynomial function below?
F(x) = x+3x2 + 4x+12

Step-by-step explanation:

When given the following function,

One is asked to find the roots. The roots of the equation are the zeros, where the graph of the equation intersects the (x) axis. To find these points on a quadratic equation (equation to the second degree -> the largest exponent in this equation is (2)), one should simplify the equation. Remember, during simplification, one is trying to get the equation of the parabola closets to the quadratic equation in standard form, this form is the following,

After simplifying the equation, one should use the quadratic formula to find the roots of the equation.

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Simplify, combine like terms, terms with the same variable to the same degree;

Now use the quadratic formula, the quadratic formula states the following,

Where the parameters (a), (b, and (c) represent the coefficients of the terms in the quadratic formula in standard form. Substitute in the respective coefficients in the given equation and solve for the roots,

Simplify,

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: