Consider the polynomial: f = 2X¹ +aX³ +3X²+bx+c € R[X] with roots X₁, X2, X3, X4 € C. a) Calculate: Σ (xi - xj)² 1

Q: Find a 3^rd degree polynomial with zeros at -2,0, and 2 that goes through the point (-4,16)

A: Given that: A polynomial has zeroes as -2, 0, 2 and passes through (-4, 16).

Q: Please create a polynomial function that has at least 3 terms, a positive leading coefficient, a…

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Q: The quadratic function that has the same shape as y=x^2 but is shifted to the right 3 units and up 2…

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Q: The number of protozoa in a biology laboratory experiment is given by the polynomial function…

A: We have The number of protozoa in a biology laboratory experiment is given by the polynomial…

Q: What are the roots of g(x)=x^2(x+4)^4(x-6)

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Q: find the real roots of f(x)=2x^3 - 11x^2 + 2x + 15 and use them to show f(x) in factored form.

A: Roots of f(x) is given below...

Q: If polynomial 4x^3 -12x^2 + kx + 4 = 0 has root at x=2. Calculate exact values of other two roots

A: As the given equation has a root x=2. Then, we need to put it, to find the value of k. , Now put x=2…

Q: if the sum of squares zeros of the quadratic polynomial f(x) =x^2-8x+k is 40. Find k

A: If the roots of ax2+bx+c=0 are m and n Then m+n=b, mn=c

Q: For the quadratic equation 9x^2+(3k+1)x+4=0 find the value(s) of k so that there is 1 real root.

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Q: If alpha and beta are zeroes of x^-x-30,then form a quadratic polynomial whose zeroes are –2alpha…

A: α & β are zeroes of x2-x-30. That is, α+β=--11  &  αβ=-301   ∵If α & β are zeroes of…

Q: 1 ) Write f(x) = x^5 + x^3 +2x^2 -12x +8 as the product of linear factors and list all the zeros of…

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Q: Faisal is trying to find the roots of the polynomial y=2x^4+6x^3+4x+4 she has correctly applied the…

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Q: Expand and state your answer as a polynomial in standard form. (4x^(4)-y^(3))^(2)

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Q: List all the possible rational rooots  for the polynomial F(X)=2x^2 -9x+3

A: By quadratic formula for roots of quadratic equation

Q: Evaluate the polynomial for the give x^(2)-5x-8;x=-4

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Q: The cubic equation, x^3 - 4x + 1 = 0 has three roots x1,x2,x3. Use transformation arguments to find,…

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Q: show that the equation x^5+2x^3+3x-4=0 has exactly one root. Justify your answer.

A: Given equation has only one root. Here is its explanation.

Q: The parabola is the graph of a quadratic polynomial p(x) = ax^2 + bx + c. A point (x0, y0) is a…

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Q: find the remainder f(x)= 2x^4-3x^3-8x+8 when devided by x-2 with showing full steps

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Q: Evalute the polynomial at x= -2    5x^4-3x^2 - x + 1 + 5x^3

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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: Given the function f(x)= 2x^4 -7x^3 -56x^2  +37x -84 and the fact that x=3/2 implies f(3/2)=0 factor…

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