Set of zeroes of a polynomial function — الرياضيات الصف الثالث الإعدادي لغات

درس «Set of zeroes of a polynomial function» فى مادة الرياضيات لـالصف الثالث الإعدادي لغات من وحدة «Algebraic fractional function and the operation on them». This lesson introduces the concept of the set of zeroes of a polynomial function, denoted as Z(f). The set of zeroes is defined as the set of all real values of x for which f(x) = 0, making it equivalent to the solution set of the equation f(x) = 0. The lesson works through seven examples to find Z(f) for various polynomial functions, including linear, quadratic, cubic, and constant functions. Key results include: a linear function like 2x - 4 has one zero {2}, a quadratic like x² - 9 has two zeros {-3, 3}, a constant function like...

الدرس ده من وحدة «Algebraic fractional function and the operation on them» فى مادة الرياضيات لـالصف الثالث الإعدادي لغات على منصة دروسات.

الدرس متاح بالاشتراك: ترم كامل أو المادة لوحدها.

ملخص الدرس

This lesson introduces the concept of the set of zeroes of a polynomial function, denoted as Z(f). The set of zeroes is defined as the set of all real values of x for which f(x) = 0, making it equivalent to the solution set of the equation f(x) = 0. The lesson works through seven examples to find Z(f) for various polynomial functions, including linear, quadratic, cubic, and constant functions. Key results include: a linear function like 2x - 4 has one zero {2}, a quadratic like x² - 9 has two zeros {-3, 3}, a constant function like f(x) = 5 has no zeros (empty set), and the zero function f(x) = 0 has all real numbers as zeros. The lesson also shows that some quadratics, like x² + 4, have no real zeros because they lead to square roots of negative numbers.

هتتعلم إيه فى الدرس ده

• Definition of the set of zeroes of a polynomial function
• Z(f) as the solution set of f(x) = 0
• Zeroes of a linear function
• Zeroes of a quadratic function by factoring
• Zeroes of a quadratic function using the quadratic formula
• Zeroes of constant functions (including zero function)
• Zeroes of higher-degree polynomials by factoring
• Polynomials with no real zeroes