Name: Date: Graded Assignment Checkup: Solving Polynomial Equations Answer the following questions using what you’ve learned from this lesson. Write your responses in the spaces provided‚ and turn the assignment in to your instructor. List all possible rational zeros for each polynomial function. 1. -3‚ 2‚ 5 2. -12‚ 17. 27 Use Descartes’ rule of signs to describe the roots for each polynomial function. 3. Two sign changes = Two or no positive roots m(-x) = (-x)3
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homogeneous constant coefficient linear equation an y (n) +· · ·+a1 y +a0 y = 0 has the characteristic polynomial an rn +· · ·+a1 r+a0 = 0. From the roots r1 ‚ . . . ‚ rn of the polynomial we can construct the solutions y1 ‚ . . . ‚ yn ‚ such as y1 = er1 x . We can also rewrite the equation in a weird-looking but useful way‚ using the symbol d D = dx . Examples: equation: y − 5y + 6y = 0. polynomial: r2 − 5r + 6 = 0. (factored): (r − 2)(r − 3) = 0. roots: 2‚ 3 weird-looking form of equation:
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arithmetic mean of the variable . Answer: < 0.8964 ‚ c) Apply the least-square regression and fit a second-order curve to the given points. Determine the standard error of estimate and the coefficient of determination. Compare the accuracy of this polynomial fit with the linear model in part (b). Answer: < 0.9567‚ > 324.8950 d) Apply the general linear least-square to fit the model ‚ where ‚ and are three basis functions as follow: ‚ ‚ Compute the corresponding matrix system by employing the method
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separate factors? distribution in what conditions can a factored expression be factored further? Greatest Common Factor A greatest common factor of two or more terms is the largest factor that all terms have in common. The greatest common factor of a polynomial should be factored out first before any further factoring is completed. Example: 3r6+27r4+15r2=3r2(r4+9r2+5) When multiplying variables‚ add the exponents. r^2•r^4=rr•rrrr=r6 When factoring a GCF‚ subtract the exponents. To factor r^2 from r^6:
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find that the trend line that fits the best is the polynomial trend line‚ which is displayed in the graph down below. If we were to analytically develop one model function to determine if the polynomial trend line is indeed the most accurate fit‚ I would propose creating a system of equations. Before jumping to far ahead‚ we need to make it clear the equation we are going to be analyzing. We will use the equation given to us by the polynomial trend line which is: y= ax2 + bx +c and the reason
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Unit 1. MATHS 1. INVESTIGATORY PROJECT TOPIC : POLYNOMIAL a) Find the possible numbers of zeroes in linear‚ quadratic ‚cubic and bi-quadratic polynomial with atleast five polynomial each. Draw graph for each case. What is your observation and what is the utility of your research? Do the Work-Sheet printed overleaf b) Examples of each polynomial will be given . Find the possible numbers of zeroes in given linear‚ quadratic and cubic polynomial and write three more examples of each and write their
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Time Frame | Objectives | Topics/ Content | Concept/s | Competencies | Teaching Strategy | Values | List of Activities | Materials | Evaluation | References | First Quarter | -Define functions and give examples that depict functions-Differentiate a function and a relation-Express functional relationship in terms of symbols y=f(x)-Evaluate a function using the value of x. | Chapter 1Functions and GraphsFunctions and Function Notations | The equation y=f(x) is commonly used to denote functional relationship
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1 MCR3U Exam Review Math Study Guide U.1: Rational Expressions‚ Exponents‚ Factoring‚ Inequalities 1.1 Exponent Rules Rule Product Quotient Power of a power Power of a product Power of a quotient Description a m × a n = a m+n a m ÷ a n = a m−n Example 4 2 × 45 = 47 5 4 ÷ 52 = 52 (a ) a m n = a m×n a a (3 ) 2 4 = 38 2 2 2 (xy) = x y an a = n ‚b ≠ 0 b b a0 = 1 a −m = 1 ‚a ≠ 0 am n (2 x 3) = 2 x 3 35 3 = 5 4 4 70 = 1 9 −2 = 4 5 Zero
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property. 1 2 Solve by quadratic formula Quadratic formula: Discriminant: x= −b ± b2 − 4ac = 0 b2 − 4ac > 0 b2 − 4ac < 0 √ −→ −→ −→ b2 − 4ac 2a one real solution two real solutions two complex solutions Solve Polynomial Equations by Factoring 1. Set to 0. 2. Factor completely. 3. Solutions are zeros of each factor: Ax + B = 0 −→ x= −B A Solve Radical Equations 1. Isolate a radical. 2. Take n-th power of both sides to get rid of radical. 3. Repeat
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Philadelphia‚ PA‚ USA April 27‚ 1997 ii Contents Foreword vii A Quick Start . . . ix I 1 Background 1 Proof Machines 1.1 Evolution of the province of human thought 1.2 Canonical and normal forms . . . . . . . . . 1.3 Polynomial identities . . . . . . . . . . . . . 1.4 Proofs by example? . . . . . . . . . . . . . . 1.5 Trigonometric identities . . . . . . . . . . . 1.6 Fibonacci identities . . . . . . . . . . . . . . 1.7 Symmetric function identities . . . . . . .
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