EXAMPLE 5 Using Square Roots of Negative Numbers Evaluate (V12 – V-3)(3 + V-4), and express the result in the form a + bi.

Q: 1. Discuss the possibilities for the roots to : 2x-5x -6x+4 = 0

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Q: A fifth degree polynomial with constant coefficients may have (1) 5 distinct real roots. (II) 3…

A: This question can be solved by using the concept of nature of roots of n degree polynomial.

Q: 1.2a-Dividing Polynomials Ha aial answer in standard form. 2x + 11x + 5 x+S

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Q: Use Bairstow's method to determine the roots of S(x)=0,1428-2,819x-0,79x+x.

A: Given function is f(x)=x3-0.79x2-2.819x+0.1428 Let initial approximation is r=0.1, s=0.1 Here a3=1,…

Q: 3. Find the roots of ( x2-1) ( x2 + 3x – 2)=0

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Q: Find a degree 3 polynomial with real coefficients having zeros 22 and 2−2i2-2i and a lead…

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Q: 16. Find a fourth degree polynomial that has the zeros 3, -2, i.

A: Given data: The first root of the polynomial is x1=3. The second root of the polynomial is x2=-2.…

Q: The positive value of k for which x2+kx+64=0 & x2-8x+k=0 will have real roots

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Q: What are all the roots of f(x) = x* – 3x³ +x – 32 A -1, 3 only 1 ti3 only 2 1tiV3 -1, 3, 2 1, -3, VI…

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Q: EXAMPLE 2.0 FIND ALL THE ROOTS OF x. (3275°- j3794)2 - 4e [(12- 42° + el30") - (2 - j5)1) (7415° +…

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Q: 9. Two zeros of f(x) = x* – 7x³ +x² – 63x – 72 are 3i and 8. In what form are the other roots? A. 1…

A: Topic = Polynomial

Q: How many zeros (including all complex zeros counted with multiplicity) does the polynomial shown…

A: Given,            y=x5-1To find: Number of zeros

Q: Find a degree 3 polynomial whose coefficient of x^3 equal to 1. The zeros of this polynomial are −3,…

A: First of all we will find the factors of this polynomial using the zeros that are given to us. We…

Q: 3. Use Graeffe's Root Squaring Method to de the real roots of the polynomial equation х3 + За? — 6х…

A: GRAEFFE'S ROOT SQUARING METHOD:   The roots of any polynomial equation with real coefficients can be…

Q: Find the equation of the polynomial with roots (–√3, 0) and (7i, 0), real coefficients, and passing…

A: Step I :   Given :   Roots : -3 , 0 & 7i , 0and passing through the point 1 , 200Find the…

Q: How many zeros (including all complex zeros counted with multiplicity) does the polynomial shown…

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Q: 6. %3D Determine the number and type of roots of g² + 10 = 3x -3.

A: GIven :  x2 + 10 = 3x -3

Q: A polynomial is given below. 3x° + 2x – x +7 | Which statement must be true about this polynomial?…

A: The degree of the polynomial is 6.  For a polynomial the maximum number of roots are equal to the…

Q: The complex zeros of f 1x2 = x4 + 1 For the function f1x2 = x4 + 1:(a) Factor f into the product of…

A: Given :            f(x) = x4 + 1

Q: 46. What are the roots of 2x - x² - 13x – 6 = 0? А. -1/2, 2, 3 В. -2, -1/2, 3 С. -2, -1, -1/2 D. -1,…

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Q: How many zeros (including all complex zeros counted with multiplicity) does the polynomial shown…

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Q: Using the given root factor completely and determine all roots 1) x' + 4x - 7x – 10 = 0; -5

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Q: Pipoline 16 30-20 shoreline Water Source.

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Q: . Prove that the equation r – x²+2x +3 = 0 has at least one real root. State the theorems or the…

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Q: O INTENATUNAL SCHUUL Find the condition for 2x² +3kx + 4c to be positive for all real values of .

A: To find the condition for 2x2+3kx+4c  to be positive for all real values of x.

Q: Prove that a fourth degree polynomial with one real root and real coefficients must have another…

A: Given: Fourth degree polynomial having one real root and if has real coefficient. To Prove: Has…

Q: f (z) = -7z4 + z2 – 25

A: This equation is about the fundamental theorem of algebra. In which for the equation shown identify…

Q: Use the Intermediate Value Theorem to show that the equation x^5-2x^3-x-1 = 0 has at least two real…

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Q: Find the roots of x^2 + (k^2+1/k) x + 1 = 0

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Q: 1- f(x) = x³ + 2x +1 has 3 roots in Z6- a) True b) False ) a) True

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Q: 3. Find the complex zeros of f(x) = x – 4x2 + 25x 100.

A: fx=x3-4x2+25x-100=x3-4x2+25x-100=25x-4+x2x-4=x-4x2+25=x-4x+5i(x-5i)

Q: Given f(x) = √ x-4,   (the square root of x-4) Use the conjugate to simplify completely f(x+h) -…

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Q: The roots of 6x2 +7x + 34 = 0 are: O Real and Equal O Real and Distinct O Complex and Unequal O…

A: To find the behaviour of the roots of the given equation.

Q: 5. Find a polynomial with real coefficients that has the zeros without complex numbers.) 4,3i, and…

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Q: Give a polynomial of degree 3 that has zeros of 18, 10i, and –10i, an the polynomial in standard…

A: Given that: Zeroes of the polynomial = 18, 10i and -10i and At x=1, y=-3434.

Q: Find a degree 3 polynomial whose coefficient of x3x3 equal to 1. The zeros of this polynomial are…

A: See the detailed solution below.

Q: Prove that a fourth degree polynomial with one real root and real coefficients must have another…

A: Since the polynomial is of 4th degree. So, it must have 4 roots . As one of the root is real . So, 3…

Q: Show the work steps for finding the roots of x- 13x+36 algebraically.

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Q: 5. What are the roots of 4x4 + 25x3 + 50x2 + 35x + 6 = 0? A. 1, 2, 3 and ¼ В. 1, 2, - 3 and - %4 %3D…

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Q: 5) Use the Intermediate Theorem and Roll's Theorem show that there is exactly one root of the given…

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Q: Separate the real roots of polynomials by Sturm's method x4-2x3+x2-2x+1

A: Sturm's method.

Q: 13. Find a polynomial of degree 4 with integer coefficient and zeros i and 3 – i (express your…

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Q: a. Find a polynomial of degree 4 that has /2 + /7 as a root. That is, find integers a, b, c, d, and…

A: For (a),  We need to find the polynomial of degree 4 that has √2 + √7 as a root. So,

Q: Suppose that R (x) is a polynomial of degree 12 whose coefficients are real numbers. Also, suppose…

A: Given,            Suppose that Rx is a polynomial 12 whose coefficients are real numbers.…

Q: PAPER 1 12015 2 The polynomial f(x)-ax-15x²+bx-2 has a factor of 2x-1 and a remainder of 5 when…

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Q: Form a polynomial with  the given roots 1+2i, 1-2i , 4 ,2

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Q: How many zeros (including all complex zeros counted with multiplicity) does the polynomial shown…

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Q: The product rule for square roots states that if a and b are nonnegative, then √ab =______.

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Q: Calculate the number of the real roots for f(x) = 44x° + 17x³ + 44x – 20 using Rolle's Theorem.…

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Q: 4. Consider the polynomial f(x) = x* + 1. (a) product of two irreducible quadratics. Explain why ƒ…

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