IX. Write a quartic polynomial function with real coefficients in expanded form that has the given zeros. 11. 0, 2, 3 + i, 3-i

Q: 16. Find the quadratic function such that f(4) = - 26, f‘(4) = -19 and f“(4) = -6.

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Q: 13. When is a polynomial f(x) of at most the order of a polynomial g(x) as x→∞? Give reasons for…

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Q: O Suppose that K.(x) JS.a POlynomial.of degree13 Whose cueffICien+s 'are' reál 'númbérs, AISO,…

A: We know if a+bi is a complex root of a real polynomial function, then it's conjugate a-bi is also a…

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Q: Q-when fitting the data shown in the table with a second order polynomial Y=a+bx+cx? The value of a…

A: Make a table for the given data as follows                x y x2 x3 x4 xy x2y 1.2 1.5403 1.44…

Q: q_2: het R = ZOZ. Showthat the polynomial has infinitely many roots. (1,0) x in R[x]

A: Let R=ℤ⊕ℤ. Show that the polynomial 1, 0x in Rx has infinitely many roots. Definition: The ring ℤ⊕ℤ,…

Q: 5.16] Use the function f (x) = xe¯ ¯x² to find fave on [0,4] %3D

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Q: Prove Viete's Formulas: The quadratic polynomial with ∝ and β as roots is     x2 +bx+ c, where b =…

A: Viete's formula relates the coefficient of the function with the roots of the function. Sum of the…

Q: a) Use Backward difference to find the Finite difference equation of the follow ди ди o'u -= C- xe…

A: We are given the equation ∂u∂t+a∂u∂x=c∂u2∂x2 , x∈ 0 , 1  , t≥0 Let us consider a grid of points in…

Q: asider the following Polynomial f(x) =x – 3.x –10x +x+11 mpute the root x-1 of the above function…

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Q: Q6) Fit a second order polynomial to the following data. Also estimate the value of y at x=1.25,…

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Q: 8. What are all the roots of the function f(x) = (x² + 1)(x – 2)? ? 2. -1 and 2 iand 2

A: solve for x over the real numbers (x^2+1)(x-2)^2=0 Split into two equations  (x-2)^2=0 or (x^2+1)=0…

Q: Q5: Find the least square polynomial approximation of the following data: 3. 9. 12 -4 -2 12 21 Hint:…

A: Using the Given hint we know y=a+bx+cx2  know we need to fit the function using Least square method…

Q: Use newton divided difference to solve the equivalent interpolation polynomial of the given below,…

A: Using Newton's Divided Difference formula to find solution x f(x) 10 227.04 15 362.78 20…

Q: [C] Obtain the interpolating polynomial of the form ax³ + bx² + cx + d (where a, b, c, d are…

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Q: Find the maximum of f(x, y) = 4y + 7xy – 4x on the square domain 0 < x < 8, 0 < y < 8. (Give an…

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Q: Find the roots of the polynomial: f (x) = a – a? +.1

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Q: Which are polynomial functions? j(x)= (3x-2)(2x+5)(x+8) f(x)=-6[2(x-1)]^3  -5 r(x)= x-1   **"X"…

A: For being a polynomial function ,power of x should be a natural number. it should not be fraction.

Q: Q3. Using interpolation, approximate the following function by a polynomial of degree at most 3…

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Q: Q 11 If P(x) is a Cx where ci are constants. polynomial, show that limaP(x) = P(a). Hint: use the…

A: To show the limit of p(x) at point a is equal to p(a).

Q: Form the polynomial function that has the following real ZEROS: 3,-1, 2, 4 Section 3.1 O z4 + 2z3 -…

A: Given point is; x = -3,-1,2,4   1) x4+2x3-14x2-13x+24  we find the factor of this function and then…

Q: Determine the 4th degree polynomial for the given set of data(x.y). 1. 1.3 2.4 3.7 3.8 5.1 y -6.3…

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Q: 3. Determine whether the functions e2a and xe2 by calculating Wronskian.

A: Let f(x) = e2x and g(x) = xe2x Then,  f'(x) = 2e2x ,and g'(x) = e2x+2xe2x (by using chain-rule of…

Q: 6. Based on your work above, and what you know about the multiplicative principle, how many…

A: The one-one function is the function each element of B  has a unique preimage of A. Also, know as…

Q: Q) Use the Lagrange interpolating polynomial of degree two to approximate f (0.43) if f (0)=1 f…

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Q: 5. Is the following set of polynomials linearly independent in P3? Explain your work. 1+ 2t³, 2 +t –…

A: As per our guidelines we are supposed to answer only first question. Please repost other question…

Q: 3. Recall that a quadratic polynomial has at most two roots. Show, using Rolle's theorem, that a…

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Q: Ques.2 Obtain the piecewise quadratic interpolating polynomial for the function f(x) define by the…

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Q: h(x) 36千 27 18- 9- -5 -4 3-2 -i 0/1 2 4 5-x 3 4 6- -18+ 27+ 36+ -45+

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Q: 12. When is a polynomial f(x) of smaller order than a polynomial g(x) as x→00? Give reasons for your…

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Q: 5) Find the velocity of rocket by using Gregory-Newton interpolation polynomial at t=260 sec. time…

A: Consider the given table. We have to find the velocityt=260 sec Since, t=260 sec is near to the…

Q: 2.3. Approximate fl1895) vising an interpolacting polynomial of degree & using Netu tons.…

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Q: [C] Obtain the interpolating polynomial of the form a³ + bx² + cx + d (where a, b, c, d are…

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Q: ow that the equation 3sin (2x) =7x+5 has exactly one real root.

A: Given:3sin2x=7x+5

Q: 6. Which of the following quadratic functions does not have zeros of -15 and 6? f(x) = -x² - 9x + 90…

A: solution

Q: 42 Which of the following polynomial functions have the largest degree? O f (x) = 107 – 22 3x + a7 –…

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Q: Q// Fit a second-order polynomial to the following data: Y 9 8 3 7 9 11 9 6 1 7 1 3 10 9. 1 a. y =…

A: Given x y 9 8 0 3 7 9 11 9 6 1 0 0 0 7 1 3 8 10 9 1

Q: Which function is a polynomial with roots x = 3, x = – 4, x = 1 ? A f(x) = (x + 3)(x +4)(x+ 1) f(x)…

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Q: Consider the quartic polynomial f(x) = + 2.5a³ + 10.5æ². 2 f(x) has two inflection points at x = C…

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Q: D. I - 1, 19. If you are asked to create a polynomial function f(x) whose roots are defined by the…

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Q: Q3. Using interpolation, approximate the following function by a polynomial of degree at most 3…

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Q: (a) Show that the quadratic function f(r) = ax² + bx+c is concave up if a > 0 and is concave down if…

A: NOTE- AS WE ARE ALLOWED TO ANSWER ONE QUESTION IN ONE SESSION SO, I HAVE ANSWERED FIRST QUESTION FOR…

Q: 1. Use the numbers x, =1 , x, = 2 and x, = 3 to find the second Lagrange interpolating polynomial…

A: We have x0=1, x1=2, x2=3 The polynomial is fx=x-2=1x2 Therefore,…

Q: Jsing MOSA find the polynomials that will approximate the solution to: y' = x2 + y; y(1)=1.

A: Y(1)=1 Solution provided

Q: 21 Q: If a, B are the zeros of the polynomial f(x)=2x +5x+k satisfying the relation a + B+ aß = %D 4…

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Q: Where is G' located if you Dilate GHI by a factor of 0.5. (1.5, 1) (1.5,- 1) (1.5, 1.5)

A: Dilation of 0.5 means the image is reduced , with its dimensions half the origin. In dilation , we…

Q: Q: A- find for the functions: - In =) + In(3x2) = In(3) %3!

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Q: W. A. Mozart’s opera Die Zauberflöte is scheduled to premiere at Theater auf der Wieden. If the…

A: This question can be solved using the concept of area under curve.