Question

# Read the following statements(a) $$x^2 - 5x+ \sqrt{2}$$ is a polynomial in x.(b) $$4x^2 - 3 \sqrt{x}+7$$ is not a polynomial in x.(c) $$\displaystyle \frac{x^2+2x+5}{x+3}(x \neq -3)$$ is a rational expression.(d) $$\displaystyle \frac{x^3 - 5 \sqrt{x} -1}{x^2 + x+4}$$ is not a rational expression.Correct options is -

A
acd
B
abc
C
abd
D
abcd

Solution

## The correct option is D abcd(a) In each term of the expression, the exponent of $$x$$ is a non-negative integer.So, it is a polynomial.(b) In the second term $$(-3 \sqrt{x})$$ of the expreesion, the exponent of $$x$$ is $$\dfrac{1}{2}$$ which is not a non-negative integer.So, it is not a polynomial.(c) Here, in $$p(x)= x^2 + 2x+5$$, the index of x in each terms is a non-negative integer. In $$q(x) = x+3$$, the index of $$x$$ in each term is a non-negative integer. Also as x $$\neq$$ 3, q(x) $$\neq$$ 0.So, it is a rational expression.(d) In p(x)$$=x^3 - 5 \sqrt{x}-1$$, the index of x in the second term $$(-5 \sqrt{x})$$ is 1/2 which is not a non-negative integer.Thus, $$p(x)$$ is not a polynomial. Therefore the given expression is not a rational expression.Mathematics

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