Some questions are asked by class 9 students related to Maths

Question 1.
Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
(i) 4x2 – 3x + 7
(ii) y2 + √2
(iii) 3 √t + t√2
(iv) y+ 2y
(v) x10+ y3+t50
Solution:
(i) We have 4x2 – 3x + 7 = 4x2 – 3x + 7x0
It is a polynomial in one variable i.e., x
because each exponent of x is a whole number.

(ii) We have y2 + √2 = y2 + √2y0
It is a polynomial in one variable i.e., y
because each exponent of y is a whole number.

(iii) We have 3 √t + t√2 = 3 √t1/2 + √2.t
It is not a polynomial, because one of the exponents of t is 12,
which is not a whole number.

(iv) We have y + y+2y = y + 2.y-1
It is not a polynomial, because one of the exponents of y is -1,
which is not a whole number.

(v) We have x10+  y3 + t50
Here, exponent of every variable is a whole number, but x10 + y3 + t50 is a polynomial in x, y and t, i.e., in three variables.
So, it is not a polynomial in one variable.

Ex 2.1 Class 9 Maths Question 2.
Write the coefficients of x2 in each of the following
(i) 2 + x2 + x
(ii) 2 – x2 + x3
(iii) π2 x2 + x
(iv) √2 x – 1
Solution:
(i) The given polynomial is 2 + x2 + x.
The coefficient of x2 is 1.
(ii) The given polynomial is 2 – x2 + x3.
The coefficient of x2 is -1.
(iii) The given polynomial is π2x2 + x.
The coefficient of x2 is π2.
(iv) The given polynomial is √2 x – 1.
The coefficient of x2 is 0.