Polynomial equations (HSC SSCE Mathematics Extension 2): Flashcards
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What are polynomial equations?
What are polynomial equations?
Expressions like ax^n + bx^{n-1} + k = 0.
Define complex numbers.
Define complex numbers.
Numbers in the form a + bi, where i = √-1.
What does the Fundamental Theorem of Algebra state?
What does the Fundamental Theorem of Algebra state?
Polynomials have as many roots as their degree.
What is a discriminant?
What is a discriminant?
A value to determine if roots are real or complex.
How do complex roots appear in polynomials?
How do complex roots appear in polynomials?
They appear in conjugate pairs for real coefficients.
What is the first step in factorising polynomials?
What is the first step in factorising polynomials?
Identify common factors in the polynomial.
What is the quadratic formula?
What is the quadratic formula?
x = (-b ± √(b² - 4ac)) / 2a.
What role do complex numbers play in applications?
What role do complex numbers play in applications?
They are vital in fields like electronics and signal processing.
What is the solution for x^2 + 1 = 0?
What is the solution for x^2 + 1 = 0?
x = i or x = -i.
Solve z^4 + z^2 - 12 = 0 for z.
Solve z^4 + z^2 - 12 = 0 for z.
z = ±2, ±√3i after factorization.