a) Show that x = 1+2i is a root of p(x) where i = surds(-1). b) By using the fact that p(x) is a polynomial with real coefficients, show by contradiction that  p(x) will have another complex root.

Q: 5. Find all the zeros for: f(x) = x3 + 2x2 - 5x - 6 6. Simplify and express with only positive…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 16) Given the function f(x)=2x –1lx² +22x–15, find all the complex roots, given that 2-i is a root.…

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Q: A quadratic polynomial y = 4x² + 7x – 3 has roots p and q. Find a quadratic g(x) = x + ax + Bwith…

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Q: find the real polynomial f(x) which has zeros x=1 (multiplicity 2) and x=2+i (multiplicity 1). you…

A: We have given the zeros x = 1 with multiplicity 2 and x = 2+i with multiplicity 1.

Q: Show that f(x) = x4 + 4.x + c has at most two real roots for any umber c.

A: Consider the given equation. fx=x4+4x+c Case 1: When c>0. No sign change, by Descartes rule of…

Q: Use Descartes’s Rule of Signs to determine the possiblenumber of positive and negative real zeros…

A: Given function is f(x)=3x^5-2x^4-2x^2+x-1Firstly,we count the number of changes in signs for the…

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Q: Let F(a) be Z2. Show that a2 and a2+a are zeros of x3+x+1.

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Q: Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the…

A: To use Descartes's rule of signs to determine the possible number of positive real zeros and the…

Q: Suppose Q is a polynomial of degree n>= 2 with distinct roots, none lying on the real axis.…

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Q: Given that x = 2 is one root of g(x) = 2x* + 4x – 9x² – 11x – 6 = 0, use factorisation to determine…

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Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.