Class 9 Exam > Class 9 Questions > Assertion (A): The expression 3x4 – 4x3/2 + x...
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Assertion (A): The expression 3x4 – 4x3/2 + x2 = 2is not a polynomial because the term –
4x3/2 contains a rational power of x.
Reason(R) The highest exponent in various terms of an algebraic expression in one
variable is called its degree.?
4x3/2 contains a rational power of x.
Reason(R) The highest exponent in various terms of an algebraic expression in one
variable is called its degree.?
Verified Answer
Assertion (A): The expression 3x4 – 4x3/2 + x2 = 2is not a polynomial ...
The assertion (A) is true, but the reason (R) is false.
The expression 3x^4 – 4x^(3/2) + x^2 = 2 is not a polynomial because one of the terms, –4x^(3/2), contains a fractional power of x. In a polynomial expression, all the exponents must be non-negative integers.
However, the reason (R) is false. The degree of a polynomial is not necessarily equal to the highest exponent in the various terms of the polynomial. The degree of a polynomial is defined as the highest exponent in the polynomial. For example, the polynomial expression x^3 + 2x^2 + 3x + 4 has a degree of 3, even though the highest exponent in the terms is 3.
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Assertion (A): The expression 3x4 – 4x3/2 + x2 = 2is not a polynomial ...
Assertion (A): The expression 3x^4 – 4x^(3/2) x^2 = 2 is not a polynomial because the term –4x^(3/2) contains a rational power of x.
Reason (R): The highest exponent in various terms of an algebraic expression in one variable is called its degree.
Explanation:
Polynomial: A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, multiplication, and non-negative integer exponents. The exponents must be non-negative integers.
Polynomials have several important characteristics, one of which is that the exponents of the variables must be non-negative integers. In the given expression, 3x^4 – 4x^(3/2) x^2 = 2, the term –4x^(3/2) contains a rational power of x, which means that the exponent is not a non-negative integer.
Therefore, the given expression is not a polynomial.
Degree: The degree of a polynomial is the highest exponent of the variable in any of its terms. It helps in determining the behavior and properties of the polynomial.
In the given expression, the term with the highest exponent of x is 3x^4. This means that the degree of the expression is 4.
Therefore, the reason provided is incorrect. The degree of a polynomial is not determined by the highest exponent in various terms of an algebraic expression, but rather by the highest exponent in any of its terms.
To summarize, the given expression is not a polynomial because it contains a term with a rational power of x. The reason provided for the assertion is incorrect as the degree of a polynomial is determined by the highest exponent in any of its terms.
Reason (R): The highest exponent in various terms of an algebraic expression in one variable is called its degree.
Explanation:
Polynomial: A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, multiplication, and non-negative integer exponents. The exponents must be non-negative integers.
Polynomials have several important characteristics, one of which is that the exponents of the variables must be non-negative integers. In the given expression, 3x^4 – 4x^(3/2) x^2 = 2, the term –4x^(3/2) contains a rational power of x, which means that the exponent is not a non-negative integer.
Therefore, the given expression is not a polynomial.
Degree: The degree of a polynomial is the highest exponent of the variable in any of its terms. It helps in determining the behavior and properties of the polynomial.
In the given expression, the term with the highest exponent of x is 3x^4. This means that the degree of the expression is 4.
Therefore, the reason provided is incorrect. The degree of a polynomial is not determined by the highest exponent in various terms of an algebraic expression, but rather by the highest exponent in any of its terms.
To summarize, the given expression is not a polynomial because it contains a term with a rational power of x. The reason provided for the assertion is incorrect as the degree of a polynomial is determined by the highest exponent in any of its terms.
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Assertion (A): The expression 3x4 – 4x3/2 + x2 = 2is not a polynomial because the term –4x3/2 contains a rational power of x.Reason(R) The highest exponent in various terms of an algebraic expression in onevariable is called its degree.?
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Assertion (A): The expression 3x4 – 4x3/2 + x2 = 2is not a polynomial because the term –4x3/2 contains a rational power of x.Reason(R) The highest exponent in various terms of an algebraic expression in onevariable is called its degree.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Assertion (A): The expression 3x4 – 4x3/2 + x2 = 2is not a polynomial because the term –4x3/2 contains a rational power of x.Reason(R) The highest exponent in various terms of an algebraic expression in onevariable is called its degree.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion (A): The expression 3x4 – 4x3/2 + x2 = 2is not a polynomial because the term –4x3/2 contains a rational power of x.Reason(R) The highest exponent in various terms of an algebraic expression in onevariable is called its degree.?.
Assertion (A): The expression 3x4 – 4x3/2 + x2 = 2is not a polynomial because the term –4x3/2 contains a rational power of x.Reason(R) The highest exponent in various terms of an algebraic expression in onevariable is called its degree.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Assertion (A): The expression 3x4 – 4x3/2 + x2 = 2is not a polynomial because the term –4x3/2 contains a rational power of x.Reason(R) The highest exponent in various terms of an algebraic expression in onevariable is called its degree.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion (A): The expression 3x4 – 4x3/2 + x2 = 2is not a polynomial because the term –4x3/2 contains a rational power of x.Reason(R) The highest exponent in various terms of an algebraic expression in onevariable is called its degree.?.
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