(i) Show that f(x) = 6x³ – 2x2 + 4x – 3 has exactly one real root. (j) Show that f (r) = x + 2x5 + 3x3 + 14.x +1 has exactly one real root.

Q: Find the zeros of the polynomial f(x) = 3 its two zeros are equal in magnitude but opposite in sign…

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Q: b.) Find the root of f(x) = 2x³-5x+2 using Method of successive substitution. (Allowable error <…

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Q: Find the roots of the quadratic polynomials: f (x) = x2 − 2x − 1

A: We know that, for an standard equation fx=ax2+bx+c, roots are calculated by using quadratic formula…

Q: Find a cubic polynomial f(x)=ax^3+bx^2+cx+d that has horizontal tangents at the points (-3,2) and…

A: Consider the given cubic polynomial fx=ax3+bx2+cx+d, it has horizontal tangents at the points (-3,2)…

Q: 1. Express the polynomial f(x) = 4x3 – 5x2 + 2x – 3 as a power of x + 2.

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Q: Show that the equation x3 - 15 x + c = 0 has at most oneroot in the interval [-2, 2] .

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Q: Find the roots of the quadratic polynomials: f (x) = 4x2 − 3x − 1

A: Given f (x) = 4x2 − 3x − 1

Q: Find the condition which must be satisfied by the coefficients of the polynomial f(x)=x3 -px2 +qx-r…

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Q: 35. Write a third-degree polynomial f(x) with integer coefficients and with zeros of -2i and.

A: Given: A third degree polynomial with integer coefficients and with zeros of -2i and 5/3. Concept…

Q: 4. Use the Intermediate Value Theorem to show that the equation 2x3 + x – 2 = 0 has a root in the…

A: The given equation is 2x3+x-2=0 has a root in the interval -1,1

Q: Find the general solution to the nonhomogeneous, lincar difference equation X+2 - 4x = 6t - 1 By…

A: Difference equation

Q: The sum of coefficients of the polynomial f(x) is equal to 2 and the sum of coefficients in even…

A: A polynomial f(x) can be represented by f(x)=a0xn+a1xn-1+...+an-2x2+an-1x+an where…

Q: Determine the real root of f(x)= -25+82x-90x2+44x3-8x4+0.7x5. Iterate until the estimated error…

A: given: fx = -25+82x-90x2+44x3-8x4+0.7x5To find root we put fx =0. ⇒-25+82x-90x2+44x3-8x4+0.7x5 = 0…

Q: Find the potential rational zero of f(x)=5x^(4)+2x^(2)-6x-5.

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Q: Which polynomial function would have the end behaviour of as x→ too, Y→ co? a) f(x) = 7x³ - 8x* -…

A: Topic = Functions

Q: Find the condition which must be satisfied by the coefficients of the polynomial f(x)=x3-px2+qx-r…

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Q: Find k so that f(x)=2x² +12x + k has one root.

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Q: Find an nth-degree polynomial function with real coefficients satisfying the given conditions as : n…

A: Since 1 and i are the zeroes of the polynomial, therefore

Q: Find the equation of a 4th degree polynomial that has zeros at x=-7x=−7,  x=2x=2,  x=3x=3  and…

A: Given that, Polynomial has zeros at x = -7, x = 2, x = 3, x = 4 and we have to find the polynomial…

Q: (c) Express the quadratic form Q(x1,x2, x3) = 6x + 3x3 + 3x3 – 4x1x2 - 2x2x3+4x3x1 %3D to the sum of…

A: A detailed solution is given below.

Q: What is the largest multiplicity in the factored polynomial y = (x2 – 1)(x + 2)(x + 4)?

A: Here function is :  y = (x2 - 1) (x +2 ) (x+4)  It can be written as  y = ( x - 1)( x + 1 )( x + 2)(…

Q: find the zeros and give the multiplicity  f(x)= (3x+2)^5(x^2-10x+25) x=               (smaller…

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Q: one of the zero of the quadratic polynomial f(x)=4x2-8kx-9 is negative of the other , then find the…

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Q: 6.6 Determine the lowest real root of f(x) = -12 - 21x + 18r - 2.4x: (a) graphically and (b) using…

A: Consider the given equation. fx=-12-21x+18x2-2.4x3 Now, make the table to find the values of the…

Q: Find the roots of the functionf(x) = (2x−1)·(x2+ 2x−3) withx∈R

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Q: In Problem,explain why the facts given are contradictory.

A: Zero of a function is a point in its domain for which the function takes the value equal to 0. A…

Q: One factor of f(x) = x^3 –8x^2 – 15x+54 is x - 2. What are the zeros of f(x)?

A: Solution of the equation

Q: Determine the real root F (x)=26+85x-91x^2+44x^3-8x^4+x^5 Graphically

A: . The real roots of an equation are the x-intercepts of the graph.

Q: 2. D- f(x) = -is not a polynomial function because %3D 2x

A: A polynomial function is a function such as a quadratic, a cubic, a quartic, and so on, involving…

Q: 3. Use Muller's method to determine the positive real root of f(x) = 9.34 -21.97x + 16.3x² - 3.704x³

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Q: 10) If x = 1 is a zero, what are the other zeros for x3 - 3x2 + x + 1 = 0 ?

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Q: Determine the real root of f(x) = 5x^3-5x^2+6x-2. Iterate until the estimated error falls equal to…

A: Given: fx=5x3-5x2+6x-2

Q: Given the function C(x) = (x – 3)( – 9x + 5)*(x – 7)°, its roots are and their multiplicities are

A: Given, C(x)=(x-3)(-9x+5)4(x-7)9

Q: Find an 4th degree polynomial function with real coefficients whose zeros are 4,–1,2, v2i and a…

A: Here degree of polynomial is 4 so it has 4 roots.

Q: could you help please help with these questions. Thank you

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Q: Use the Intermediate Value Theorem to show that the equation x6 − 8x4 + 10x2 − 1 = 0 has at least…

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Q: The polynomial of degree 33, P(x)P(x), has a root of multiplicity 22 at x=3x=3 and a root of…

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Q: Determine the real root of f(x)=x4-8x3-35x2+450x -1001. Using false-position method to locate the…

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Q: Find a zero of f(x)=9x3 - 10x +1 by finding a fixed point of x=g(x)=0.9x³+0.1. %D

A: see  below the calculation and answer

Q: Use the intermediate value theorem to show that f(x) = 4x^3 - 6x^2 + 3x - 2 has a root between x = 1…

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Q: Find the critical number of f(x) = 3x^2 - 18x + 4

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Q: Prove that the equation x- 15x +k = 0 has at most one root in the interval [-2, 2]. Hint: You'll…

A: Dear friend,  if you have any other query about this problem, then please tell me about your query I…

Q: Determine the real root of f(x)=5x3-5x2+6x-2. Iterate until the estimated error falls equal to or…

A: MOSS:- Method of successive substitution Given that fx=5x3-5x2+6x-2 For Real root put fx=0…

Q: Determine the first root of: f (x) = –13 – 20x + 19x2 – 3x³ using graphical method

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Q: Find all zeros of f(x)=x³ + 5x² – 4x – 20 %3D -

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Q: Q1: Prove that the equation x2 = 7 has a unique positive real root. %3D

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Q: 9. For the polynomial function f(x)= x³ - bx² + cx-24 where b,cel, all of the following are…

A: The given function is a cubic polynomial: f(x)=x3-bx2+cx-24     , here b,c∈I If p is a zero of that…

Q: a) f(x)=-x- 13x²+3x – 9 Туре of polynomial Degree Sign of leading End behaviours Domain сoefficient

A: given that f(x)=-14x3-13x2+3x-9

Q: Find an equation with real coefficients for the polynomial that passes through the point (0,…

A: we have to find an equation with real coefficients for the polynomial that passes through the point…