which of the following expressions are polynomial in one variable and which are not? give reason for your answer. b) 2√x+√2x+3
Answers
Answer:
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Answer:
i) `4x^2 -3x + 7`
Answer: Since, the given expression has only one variable ‘x’, hence this is a polynomial in one variable.
(ii) `y^2 + sqrt2`
Answer: Since, the given expression has only one variable ‘y’, hence this is a polynomial in one variable.
(iii) `3sqrt\t + t\sqrt2`
Answer: Since, variable, ‘t’ in this expression exponent of variable is not a whole number. [Exponent of a variable in a polynomial must be a whole number. Expression with exponent of a variable in fraction is not considered as a polynomial.]
(iv) `y + 2/y`
Answer: Since, exponent of the variable is negative integer, and not a whole number, hence it cannot be considered a polynomial.
(v)
x
10
+
y
3
+
t
50
Answer: Since, given expression has three variables, i.e. x, y and t, so it is not a polynomial in one variable.
Question 2: Write the coefficients of x2 in each of the following:
(i)
2
+
x
2
+
x
Answer: Given;
2
+
x
2
+
x
Here, coefficient of
x
2
=
1
(ii)
2
–
x
2
+
x
3
Answer: Here, coefficient of
x
2
=
1
(iii)
π
2
x
2
+
x
Answer: Here, coefficient of
x
2
=
π
2
(iv)
√
2
x
–
1
Answer: Here, coefficient of
x
2
=
0