Question

Assertion: The expression $3x^4-4x^{\frac{3}{2}}+x^2$ is not a polynomial because the term $-4x^{\frac{3}{2}}$ contains a rational power of x.

Reason: The highest exponent(of the variable) in various terms of a polynomial in one variable is called its degree.

Which of the following is true?

• A. Both Assertion and Reason are true and the reason is the correct explanation for the assertion.
• B. Both Assertion and Reason are true, but the reason is not the correct explanation for the assertion.
• C. Assertion is true and Reason is false.
• D. Assertion is false and Reason is true.

Answer 1

The correct option is B

Both Assertion and Reason are true, but the reason is not the correct explanation for the assertion.

Expression $3x^4-4x^{\frac{3}{2}}+x^2$ is not a polynomial because the power in the term $4x^{\frac{3}{2}}$ is $x^{\frac{3}{2}}$ where $\frac{3}{2}$ is not a whole number.

The highest exponent in various terms of a polynomial in one variable is called its degree.

As we can see, both the assertion and reason are true. But the statements are independent of each other. The statement mentioned in "Reason" does not mention the reason why the expression $3x^4-4x^{\frac{3}{2}}+x^2$ is not a polynomial.