quadratic polynomials‚ see Quadratic polynomial. A quartic equation is a fourth-order polynomial equation of the form. A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. Monomial – is a polynomial with only one term. Binomial – is polynomial with two terms. Trinomial – is a polynomial with four or more terms. Polynomial – is a polynomial with three terms. Constant – a polynomial of degree
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Find a quadratic polynomial‚ the sum and product of whose zeroes are 0 and √5 respectively. 2. Find the quadratic polynomial‚ the sum and product of whose zeroes are 4 and 1‚ respectively 3. If a and b are the zeros of the quadratic polynomial f(x)= x2-5x+4‚ find the value of 1/a + 1/b-2a b 4. Find the zeroes of the quadratic polynomial 4√3 x2+ 5 x - 2 √3 and verify the relationship between the zeroes and the coefficients. 5. Find the zeroes of the quadratic polynomial 4u2+ 8u and verify
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2.2.1 Reed-Solomon Codes Irving Reed and Gus Solomon [37] on January 21‚ 1959‚ submitted a paper which was published in June 1960 in the Journal of the society for Industrial and Applied mathematics with the title “Polynomial codes over certain finite fields”. This paper introduced a new class of error correcting codes that are now called Reed-Solomon codes. Reed-Solomon codes[38][39] are constructed and decoded by using finite field arithmetic. Finite fields were the discovery of French mathematician
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Module Two Pretest 02.01 Rational Exponents 02.02 Properties of Rational Exponents 02.03 Solving Radical Equations 02.04 Module Two Quiz – EXEMPTED ITEM‚ Please skip 02.05 Complex Numbers 02.06 Operations of Complex Numbers 02.07 Review of Polynomials 02.08 Polynomial Operations 02.09 Module Two Review and Practice Test 02.10 Discussion-Based Assessment 02.11 Module Two Test 03.00 Module Three Pretest 03.01 Greatest Common Factors and Special Products 03.02 Factoring by Grouping 03.03 Sum and Difference
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Checkup: Polynomial Expressions Answer the following questions using what you’ve learned from this unit. Write your responses in the space provided‚ and turn the assignment in to your instructor. State the degree of each polynomial. 1. _6_ 2. _10_ 3. _3_ Classify each expression as a polynomial or not. If the expression is a polynomial‚ name it according to its degree and its number of terms. 4. Not a Polynomial 5. Quintic Polynomial 6. Not a Polynomial
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answer. I. MULTIPLE CHOICES Directions: Read the following test items carefully. Write the letter of the correct answer. 1. Which of the following is a polynomial function? a. P(x) = 3x-3 – 8x2 + 3x + 2 c. P(x) = 2x4 + x3 + 2x + 1 b. P(x) = x3 + 4x2 + – 6 d. G(x) = 4x3 – + 2x + 1 2. What is the degree of the polynomial function f(x) = 5x – 3x4 + 1? a. 2 c. 4 b. 3 d. 5 3. What will be the quotient and the remainder when y = 2x3 – 3x2 – 8x + 4 is
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Algebra Archit Pal Singh Sachdeva 1. Consider the sequence of polynomials defined by P1 (x) = x2 − 2 and Pj (x) = P1 (Pj−1 (x)) for j = 2‚ 3‚ . . .. Show that for any positive integer n the roots of equation Pn (x) = x are all real and distinct. 2. Prove that every polynomial over integers has a nonzero polynomial multiple whose exponents are all divisible by 2012. 3. Let fn (x) denote the Fibonacci polynomial‚ which is defined by f1 = 1‚ f2 = x‚ fn = xfn−1 + fn−2 . Prove that the inequality 2 fn
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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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