Topic #6: Polynomial Equations

Topic #6: Polynomial EquationsDrillFind the zeros of the following function (in factored form)

Find a quadratic equation (in polynomial form) with zeros at -3, and 4.

Factor the following polynomial equation, then identify the zeros:

Topic #6 ObjectivesAfter completing the topic Polynomial equations, students will be able todefine and use imaginary and complex numbers in the solution of quadratic equations; use the discriminant of a quadratic equation to determine the number and type of roots of the equation; understand the implications of the Fundamental Theorem of Algebra and the Remainder Theorem, and solve quadratic and higher degree polynomial equations.

Vocabulary for Topic #6quadratic formula, imaginary numbers, complex numbers, discriminant, real roots, and complex roots

Extra Credit vocabulary due Friday!DrillSolve each equation.

DrillSolve the following equations. (Factor and find the zeros)

DrillSolve the following equations.

DrillFind the vertex (min/max) and zeros of the following function:1. Solve the following equations: (you may round answers to the nearest hundreth)

2.

3.

Word Problem PracticeA company plans to build a large movie theatre. The financial analyst determined that the profit function for the theatre was where x is the number of movie theatres and P(x) is the profit earned in thousands of dollars. Determine the range of numbers of movie screens that will guarantee a profit.

Word Problem Practice #2During practice, a softball pitcher throws a ball whose height can be modeled by the equation h = -16t 2 + 24t +1, where h = height in feet and t = time in seconds. At what time(s) does the ball reach a height of 6 ft?Word Problem Practice #3The height of a javelin (in feet) is modeled by the equationwhere t is the time in seconds after the javelin is thrown. How long is the javelin in the air?

DrillSolve the following equations.

DrillSimplify each expression.

Drilla. Find the discriminant. b. Identify the number and types of roots. c. Find the solution(s).

The discriminant and solutions*Value of the discriminantNumber and type of solutionsGraph>0 (positive)Perfect square2 real, rational roots2 x-intercepts>0 (positive)

2 real irrational roots2 x-intercepts= 0 1 real (rational) rootVertex on the x-axis