Polynomials : Algebraic Division and Complex Roots
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The polynomial:
4x^4 - 6x^3 + 4x^2 - 3x + 1 has the real roots at x = 1 and x = 1/2 and two complex conjugate roots.
(a) by the process of algebraic division and then solving a quadratic equation, find the complex roots.
(b) Write down all the factors of the 4th degree polynomial
4x^4 - 6x^3 + 4x^2 - 3x + 1
(c) Find the gradient of the curve y = 4x^4 - 6x^3 + 4x^2 - 3x + 1 at the point where x=2.
(note - x is the letter x)
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Solution Summary
Algebraic division of a polynomial and complex roots are found. The process of algebraic division and then solving a quadratic equation is examined.
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The polynomial:
4x^4 - 6x^3 + 4x^2 - 3x + 1 has the real roots at x = 1 and x = 1/2 and two complex conjugate roots.
(a) By the process of algebraic division and then solving a quadratic equation, find the complex roots.
Since x=1 and x=1/2 are roots, (x-1)(2x-1)=2x^2-3x+1 divides the given polynomial ...
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