Theorem: Every polynomial ax? + bx + c has two unambiguous roots over C (the Complex Numbers). Choose all the assumptions that are needed in order for this Theorem to be true. No additional assumptions are needed. The Theorem is true as stated. O a +0 6² – 4ac > 0 O 62 – 4ac < 0 O 62 – 4ac = 0

Q: (a) Given that 2+i is a complex root of the cubic polynomial r³ −11x+20, determine the other two…

A: Given that is one root of the cubic polynomial  , so we have to find the other two roots of the…

Q: Prove this theorem Let a,b,c be an element of real numbers where a is not equal to zero. The…

A: Use the provided information.

Q: Which of the following polynomials has zeros 3 + 2i and 3-2i? O x² 6x + 5 O x? + 6x – 5 O x? - 6x +…

A: We Know that Zeros of a polynomial can be defined as the points where the polynomial becomes zero as…

Q: Let P(x) = x6-117x3-1000 (a) Find all Zeros Of P, real and complex. to (6.) Factor R completely with…

A: Solution- Given Equation - P(x) = x6-117 x3-1000…

Q: In the diagram, ABDE is a rectangle, ABCD is equilateral, and AD is parallel to BC. Also, AE = 2x…

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Q: 6 Match the following quadratics to their zeros. x² + 10x + 21 = 0 x² + 76x + 75 = 0 x² + 32x + 31 =…

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Q: Divide the polynomials by using an appropriate method. (8x" – 16k10 + 24k° – 32k*) + (84®) = O olo

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Q: Exercise Find the roots of x2 – 3ix + (-3+i).

A: Topic = Algebra

Q: Find all the real roots of given that 121/2/2 7 is one of them. p(x) = 7x³ + 19x² - 2x - 24

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Q: Find all (real) values of b and e such that a³ + bx²y + cxy² + 4y³ +6x +3 с is harmonic on all of C.

A: The given function is .The aim is to find the value of  and  for which the function is harmonic for…

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

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Q: Verify that z 2 + 4i is a solution of z2 + 6z - 40i = 0. Is 2+ 41 also a solution?

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Q: When a is a positive real number, the ________ ________ root of −a is defined as √−a = √ai.

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