- #1
Vitani11
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Homework Statement
z2-(3+i)z+(2+i) = 0
Homework Equations
The Attempt at a Solution
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Does the quadratic formula work in this case? Should you deal with the real and complex parts separately?
Vitani11 said:Homework Statement
z2-(3+i)z+(2+i) = 0
Homework Equations
The Attempt at a Solution
[/B]
Does the quadratic formula work in this case? Should you deal with the real and complex parts separately?
Complex coefficients in a polynomial are numbers that involve the imaginary unit, i, which is equal to the square root of -1. These coefficients are part of the algebraic expressions in the polynomial and can be written in the form of a + bi, where a and b are real numbers and i is the imaginary unit.
To find the roots of a polynomial with complex coefficients, you can use the same methods as finding the roots of a polynomial with real coefficients. This includes factoring, the quadratic formula, and using synthetic division. However, the roots may be complex numbers rather than real numbers.
Yes, a polynomial with complex coefficients can have real roots. In fact, for a polynomial with complex coefficients, the number of complex roots is equal to the degree of the polynomial. This means that if the degree is odd, then there will be at least one real root.
Yes, it is possible to have repeated roots in a polynomial with complex coefficients. Just like with polynomials with real coefficients, if the discriminant is equal to 0, then there will be repeated roots in the polynomial.
The complex roots of a polynomial affect the graph by creating turning points or inflection points. The graph will still intersect the x-axis at the complex roots, but it will not cross the x-axis at these points. Instead, it will change direction and continue on its path.