Assertion :Degree of the polynomial $5 x^{2} + 3 x + 4$ is $2$ . Reason: The degree of a polynomial of one variable is the highest value of the exponent of the variable.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct, but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
By definition of degree of a polynomial in one variable is the highest value of the exponent of the variable.
Here, $5 x^{2} + 3 x + 4$ is a polynomial in $x$ , which has $2$ as the highest power.
Therefor the degree is $2$ .

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Similar questions

Q. Assertion: The expression

3 x^{4} - 4 x^{\frac{3}{2}} + x^{2}

is not a polynomial because the term

- 4 x^{\frac{3}{2}}

contains a rational power of x.
Reason: The highest exponent in various terms of an algebraic expression in one variable is called its degree.
Which of the following is true?

Assertion: The expression $3 x^{4} - 4 x^{\frac{3}{2}} + x^{2}$ is not a polynomial because the term $- 4 x^{\frac{3}{2}}$ 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?