Find all the real roots of the following polynomial equation: 1) (3x + 2) (x² - 25) = 0 2) 2x³ – 3x² – 8x + 12 = o 3) 3xª + 5x3 - 28x2 + 4x + 16 = 0

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 integral zeros of the following polynomial equations. 1. x-19x - 30 = 0 2. x + 5x2 - 2-…

A: we solve this problem using synthetic division, look at step 2

Q: I the zeros of the given quadratic polynomials, and verify the relationship between the oefficient…

A: Explanation and solutions is given below.....

Q: If a + bi is a root of a polynomial equation with real coefficients, b + 0, then. equation. is also…

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Q: Find all the solutions to the polynomial: x* + 4x°+7x² + 16x + 12 = 0 1 -4 -2i O 2i -3 O -1

A: A polynomial function is a function that involves only non-negative integer powers or only positive…

Q: Find the zeros of the polynomial f(x) = 4/3x +5x-23, and verify the relationship between the zeros…

A: we have givenf(x) =43x2 +5x-23for finding zeros of this polynomial f(x) =0

Q: Find all the real roots of the following polynomial equation. 1.) (3x+2)(x2-25)=0 2.)…

A: As per bartleby guidelines we only give first question answers.

Q: Find a fourth degree polynomial that has zeros of 1,-3,2i

A: The zeros of the polynomial are 1, -3, 2i. Since 2i is the zero of the polynomial, therefore its…

Q: Find a fourth degree polynomial with real coefficients that has zeros of -3, 2, i that passes…

A: Let us consider a fourth-degree polynomial:

Q: Find the zeros of the polynomial f(u) = 4u + 8u, and verify the relationship between the zeros and…

A: f(u) = 4u2 + 8u To Find the zeros of the polynomial f(u) and To verify the relationship between the…

Q: Find the roots of the polynomial: f(x) = 3xª+5x³+20x² +30x+12.

A: fx=3x4+5x3+20x2+30x+12

Q: Find the zeroes of the quadratic polynomial x2+7x+10, and verify the relationship between the zeroes…

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Q: Give a polynomial equation with integral coefficients that has the following roots. 2, 3, 1/2

A: we can write polynomial as product of roots

Q: must every polynomial equation with real coefficients of degree 3 have at least one real root? Why

A: Recall: Fundamental theorem of Algebra: Any polynomial of degree n with real coefficient has n…

Q: The polynomial x4 - 4x³ +7x² − 16x + 12 has four zeros: two nteger zeros and two complex zeros.…

A: Follow the procedure given below.

Q: Consider 2x3+3x2-x+7=0 where α, β, γ are roots.  Find α2β+β2α+γ2β+β2γ+α2γ+γ2α

A: Given, 2x3+3x2-x+7=0

Q: Solve the polynomial 5x* - 16 + 3x2 + 20x - 4 = 0, given that 2 is a root of multiplicity 2.

A: Given polynomial is : 5x4-16x3+3x2+20x-4 = 0 The root x=2 has multiplicity 2.

Q: 2) x- 7メ r Sx3 +93 ×2 イ2x-72=0 R) x5-2x4 -15x°t 10×*+イX-18=0

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Q: Find the polynomial equation of lowest degree, with real coefficients and leading coefficient 1 that…

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Q: Verify that 3,-1 and -1/3 are the zeros of the cubic polynomial p(x) =3x2-5x2-11x-3 and them verify…

A: Please refer to the image below

Q: Find the roots of the quadratic polynomials:(a) f (x) = 4x 2 - 3x - 1 (b) f (x) = x 2 - 2x - 1

A: We set them equal to 0 and solve for x we first factor the left side then we set each factor equal…

Q: The term containing the highest power of x in the polynomial f (x) is 6x. One of the roots of the…

A: Given the quadratic polynomial x2-2x+3 is a factor of f(x) and the highest power of f(x) = 3 Let…

Q: Verify that 3,-1 and -1/3 are the zeros of the cubic polynomial p(x) =3x2-5x2-11x -3 and then verify…

A: Note :- Solved by taking cubic polynomial p(x) = 3x3-5x2-11x -3 ( because in cubic polynomial 'x'…

Q: Find a fourth degree polynomial that has zeros of 1, -3, 2i.

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Q: Find the equation of the polynomial with roots √2 and -5i, real coefficients, and passing through…

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Q: 2)(x°tx -35)(x2 -ext 1a) Lxス+axー27) =D0 2) Cax2 +SX -う)(3x<+5X-2) [xミ qxt 10) =0 3) Casx2-1) (xメ-…

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Q: Give a polynomial equation with integral coefficients that has the following roots. ±2 , ±3

A: To give a polynomial equation with integral coefficients that has the following roots.±2 , ±3

Q: 4) -3, -4, 5 ansurer -2 -3 3 answer 6) - answer .

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Q: Choose only one method under the LU Factorization Method to find the roots of the following set of…

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Q: Find the roots of the quadratic polynomials: 6x^2+5x−1 4x^2+4x−4

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Q: Find the zeroes of the polynomial x2-3 and verify the relationship between the zeroes and the…

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Q: 1. Write the equation to the polynomial with double roots at 3 and 6, that levels off as it passes…

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Q: b) Find all the roots of x3+7x²+7x+1%3D0

A: First find the one root by hit and trial method then using long division form the quadratic and…

Q: Determine the real roots of the equation using open methods (Error≈0.001): f(x) = - 24 + 80x - 90x2…

A: According to the fundamental theorem of algebra, every algebraic equation has a root. The derivative…

Q: Create a polynomial equation with real coefficients that has 2 and 1-i as roots.

A: To create a polynomial equation with real coefficients that has 2 and 1-i as roots.

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

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Q: Show that the equation r1 + x³ + 4x – 2 = 0 has exactly one real root.

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Q: 29. Select the quadratic polynomial with roots –1 and 4. x2 + 3x – 4 x3 – 2x2 – 7x – 4 4x² + 8x + 4…

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Q: Determine the roots of f(x) = -12- 12x + 18x² - 2.75x³ a. Graphically

A: A. Hint: The given equation is f(x)=-12-12x+18x2-2.75x3. Differentiate the given function with…

Q: A fourth-degree polynomial with real coefficients canhave −5, −8i, 4i, and 5 as its zeros.

A: Given the statement that a fourth degree polynomial has real coefficients can have  -5 ,-8i 4i and 5…

Q: 3. If x=-2 is one of the roots of 6x'+11x - 4x -4 = 0, find the other two roots of the polynomial…

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Q: If a + bi is a root of a polynomial equation with real coefficients, b ≠ 0, then________ is also a…

A: Given: if a+bi is the root of a polynomial equation with real coefficients,b≠0, then ..............…

Q: Show that a cubic polynomial x3 + Ax2 + Bx + C has one real zero and two pure imaginary zeros only…

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Q: Find a polynomial f(x) of degree 5 that has the following zeros. -4, -1, 6 (multiplicity 2), 0 Leave…

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Q: Find a polynomial of degree 4 with integer coefficients that has -2 as its only real zero and (1/3)i…

A: A polynomial of degree 4 with integer coefficients that has -2 as its only real zero. Which implies…

Q: Determine the roots of f(x) = -12- 12x + 18x² -2.75x³ a. Graphically

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Q: 2. Determine the exact real roots for the polynomial equations. a) 8x¹ + x = 0 b) x³ = 5x - 4

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Q: Calculate the roots of the following polynomial equations: (a) x – 6x2 + 1lx – 6 = 0 given x = 1 is…

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Q: Give a polynomial equation with integral coefficients that has the following roots. 1± 2i, 2±√3

A: We can solve the problem by just multiply the factor of the polynomial.

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…