Question bank: Polynomials: Girard's Relations

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Question 1:

Hard

Polynomials: Girard's Relations

Question 2:

Medium

Polynomials: Girard's Relations

Question 3:

Easy

A box manufacturer wants to create a new packaging for their products. The shape of the box is defined by a polynomial that represents the volume V(x) of the box as a function of the height x of the square base. The polynomial describing the volume of the box is given by V(x) = x^3 - 6x^2 + 9x. To optimize the use of material, the company wants to determine the height of the base that maximizes the volume of the box. Use Girard's relations to find the sum of the roots of the polynomial V(x). Then, determine the height x that maximizes the volume of the box. (Consider that the value of x is positive and that the unit of measure of the height is the same as the square base, so it does not interfere with the optimization analysis).

Polynomials: Girard's Relations

Contextualized Question

Calculus Question

Question 4:

Medium

A rocket manufacturer has developed a model with a parabolic base, which ensures better aerodynamic performance during launch. The rocket was designed according to a parabolic equation y = ax² + bx + c, where a, b, and c are real constants. The coordinates of the vertex and the intersection of the symmetry plane with the base, which is the point of opening of the parabola, were collected and it was identified that the vertex of the parabola has coordinates (3, 1) and the intersection point of the plane with the base has coordinates (4, 5). Use Girard's Relations to step by step find the equation of the rocket in terms of the axis, with x as the vertical symmetry axis and y as the height.

Polynomials: Girard's Relations

Question 5:

Medium

Polynomials: Girard's Relations

IARA TIP

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