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The number of zeroes, the polynomial f(x) = (x - 3)² + 1 can have is?
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The number of zeroes, the polynomial f(x) = (x - 3)² + 1 can have is?
Number of Zeroes of a Polynomial
The number of zeroes a polynomial can have is determined by the degree of the polynomial. In this case, the polynomial given is f(x) = (x - 3)² + 1.
Definition of Zeroes of a Polynomial
The zeroes of a polynomial are the values of x for which the polynomial evaluates to zero. In other words, they are the solutions to the equation f(x) = 0.
Quadratic Polynomial
The given polynomial f(x) = (x - 3)² + 1 is a quadratic polynomial because the highest power of x is 2.
Quadratic Polynomial Zeroes
A quadratic polynomial can have at most 2 zeroes. However, in this case, the given polynomial does not have any real zeroes because the expression (x - 3)² is always greater than or equal to zero, and adding 1 to it will never make it zero.
Conclusion
Therefore, the polynomial f(x) = (x - 3)² + 1 has no real zeroes. This means that the polynomial does not intersect the x-axis and does not have any real solutions.
The number of zeroes a polynomial can have is determined by the degree of the polynomial. In this case, the polynomial given is f(x) = (x - 3)² + 1.
Definition of Zeroes of a Polynomial
The zeroes of a polynomial are the values of x for which the polynomial evaluates to zero. In other words, they are the solutions to the equation f(x) = 0.
Quadratic Polynomial
The given polynomial f(x) = (x - 3)² + 1 is a quadratic polynomial because the highest power of x is 2.
Quadratic Polynomial Zeroes
A quadratic polynomial can have at most 2 zeroes. However, in this case, the given polynomial does not have any real zeroes because the expression (x - 3)² is always greater than or equal to zero, and adding 1 to it will never make it zero.
Conclusion
Therefore, the polynomial f(x) = (x - 3)² + 1 has no real zeroes. This means that the polynomial does not intersect the x-axis and does not have any real solutions.
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The number of zeroes, the polynomial f(x) = (x - 3)² + 1 can have is?
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The number of zeroes, the polynomial f(x) = (x - 3)² + 1 can have is? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The number of zeroes, the polynomial f(x) = (x - 3)² + 1 can have is? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of zeroes, the polynomial f(x) = (x - 3)² + 1 can have is?.
The number of zeroes, the polynomial f(x) = (x - 3)² + 1 can have is? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The number of zeroes, the polynomial f(x) = (x - 3)² + 1 can have is? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of zeroes, the polynomial f(x) = (x - 3)² + 1 can have is?.
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