8. The polynomial 2 + 3x? - x can be expressed as a linear combination of the set (1, x, x, x, x) False True

Q: Let p > 2 be a prime number. If f(x) = 1' + x* + x² - x +1 € Z,[F] is divisible by the polynomial z…

A:

Q: The sum of two positive real numbers x and y is 6. Find an x and y among these such that the product…

A: We need to find x and y.

Q: polynömial that passes through the three points (0, 1), (1, 2) and (2, 23). If the coefficient of x…

A:

Q: a. Give the smallest extension of Q that contains all the zeros of x4 - 2x2 – 15.

A: We shall answer first question only as you have asked diff question without mentioning. For others…

Q: Write a general polynomial q(z) of degree n with coefficients that are bo, b,, b2, ..b,. What are…

A:

Q: Suppose that ƒ'(x) = 2x for all x. Find ƒ(2) if ƒ(-2) = 3.

A:

Q: 19) Determine a polynomial that represents the area of a square having sides of length s x + 8. B)…

A:

Q: Determine the linear interpolating polynomial that passes through the points (2,4) and (5,1). p(x) =…

A:

Q: 1. Use polynomial fitting to find a closed form for 5, 8, 13, 20, 29, ...

A: Given , Sequence = 5,8,13,20,29,.....   To find: Closed form of sequence i.e. formula for nth term .

Q: The sum of two positive real numbers x and y is 6. Find an x and y among these such that the product…

A:

Q: 16. As a generalized interpolation problem, find the quadratic polynomial q(x) for which q(0) = -1,…

A: let the polynomial q(x)=ax2+bx+c q'(x)=2ax+b since q(0)=-1(given) a(0)+b(0)+c=-1⇒c=-1

Q: The sum of two positive real numbers x and y is 3. Find an x and y among these such that the product…

A:

Q: 1 Expand f (2) = in the domain 2 < |z| < 14 (z-2)(z-14)

A: Follow the procedure given below.

Q: The sum of two positive real numbers x and y is 12. Find an x and y among these such that the…

A: The sum of two positive real numbers x and y is 12.

Q: (b) Show that factorial polynomial corresponding to P,- k³ – 4k* + 2k³ – k² + k + 10 is P, = k(5) +…

A: Given: The given polynomials is Pk=k5-4k4+2k3-k2+k+10, To prove Pk=k5+11k4-k3-9k2-k1+10

Q: x : x is a natural number less than 10​}

A: Write in explicit form

Q: Suppose z1 = 2+j, z2 = 3-j2 and z3 = -+j. Evaluate 23+2-5-1 2-+3-3 %3D

A:

Q: 32. If p(x) is a polynomial in Z,[x] with no multiple zeros, show that p(x) divides xP" . x for some…

A: Let F be a field, and suppose p(x) ∈ F[x]. hp(x)i is the set of all multiples (by polynomials) of…

Q: 1. It is known that the polynomial p(x) = 2 – (x + 1) + x(x + 1) – 2æ(x + 1)(x – 1) interpolates the…

A: Solution by using Newton's forward difference interpolation method .

Q: Let S = – 5,1 – 2x2, p(x) }. For which polynomial p(x) the set S spans P2? Select one: O 2x + x O 2x…

A: The span of a set of vectors is the set of all linear combinations of the vectors.

Q: Then by using "Newton's interpolating polynomial method", the scientist got the following polynomial…

A:

Q: 7. Ifa, Band y are the zeroes of the polynomial p (x) = ax'+ 3bx² + 3cx+ d and having relation 2B =…

A:

Q: Show that f 1 (3) does not exist.

A: Given : To show f'(3) doesnot exists

Q: 43. Show that there cannot exist rational numbers a, b such that V3 = a+b/2.

A:

Q: Prove that ax² bx C + + (x − a) (x −b) (x −c) (x-b) (x-c) x-c -+1 x³ 3 (x-a)(x-b)(x-c)

A:

Q: 5. Show that Ax) = Inx² - 1- In/3, if f'(x)= and (2) = 0. x- 1 Justify your answer.

A: To show that f(x)=ln|x²-1|-ln√3

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+

A:

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: 10-If p is a prime number, then in Z[x] the polynomial x -1 –1 = a) (x - 1) (x + 2) (x –- 3)... (x +…

A:

Q: If a, Band y are the zeroes of the polynomial p (x) = ax'+ 3bx² + 3cx+ d and having relation 2B =…

A: Option (c) is correct.

Q: Indicate the least integer n such that f(x) = (3æ³ + 2x²)(5æ5 + 4æ*) € O(x").

A: Finding f(x) explicitly using multiplication of polynomial. The highest power of x or degree of f…

Q: Verify the assertion made in Example 2.

A:

Q: Write the polynomial f(x) that meets the given conditions. Degree 3 polynomial with interger…

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Q: 5. Find the v alue of x. 5x – 4 x + 6

A: Given :    To determine : The value of x.

Q: 1 If f(x, y, z)= of then x- y- 3z ду а. 1 (х— у-3-)* b. -1 | (х-у-3-)? С. (х — у-3-)? d. 1 (х-у-3-)2

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Q: 4. Which of the following describes the end behavior of the polynomial y = -x+ x? A as x -oo, y 00…

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Q: -21 -42 -63 -84 -105 -126- -147 -168- -189- -210 For the above quartic polynomial f( x ) = 1.5a –…

A: To find the interval on which f(x) is concave down.

Q: 2-Suppose that you have n data points (x1, y1), ..., (xn, yn), with the xi all distinct. Which of…

A: Question 2 is related to Existence and Uniqueness of interpolating polynomials Question 3 is asking…

Q: Prove that ax² bx + (x − a) (x −b) (x −c) ¹ (x − b) (x − c) || x³ 3 (x-a)(x-b)(x-c) C +—+1 X-C

A:

Q: Lee 5.1 Write He nterp polynomial mlerpolat ing the ponts x,-0, x=l, x;=4 for fLx)=e* on@ [0, 4].…

A: The formula to find a polynomial using Lagrange's interpolation is: f(x) =…

Q: 17. Find the solution to the interpolation problem of finding a polynomial q(x) with deg(q) < 2 and…

A:

Q: Suppose that ƒ'(x) = 2x for all x. Find ƒ(2) if ƒ(1) = 0

A: We have, f'x=2x Integrating both of the side with respect to x, we get the result as…

Q: Find all integer x satisfying the condition x gcd(4x +3, 2x). Justify your answer. %3D

A:

Q: 17. Find the solution to the interpolation problem of finding a polynomial q (x) with deg(q) < 2 and…

A:

Q: Maximize Z = 2x, + 3.x2; st. 5x, + 7x, <35, 4x, +9x, < 36, X1,X2 2 0 and are intergers

A:

Q: 15. Show that (x+ 5) is a factor of f(x) =x3 -x² -21x + 45 then factor f (x) completely.

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Q: +an then A" P. - aon!. If P, be a polynomial of degree n, i.e., Pa = aok" + a;k"-1 +..

A: To Prove :-  If Pk be a polynomial of degree n  , i.e. , Pk = a0 kn + a1 kn-1 + ..............+ an ,…

Q: 24. Determine the number of zeroes of the polynomial z7 – 6z5 + 8 in the annulus 1 < |z| < 2.

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: