Question

VIALS
EXERCISE 4.1
Which of the following expressions are polynomials in
not? State reasons for your answer.
4x2 – 3x +7
(ii) y2 + 2
(iii) 3Vt +
) xlo + y2 + 50​

Answer 1

Answer:

(i)4x2 – 3x + 7

there is only one variable x with whole number power so this polynomial in one variable

(ii)y2 + √2

there is only one variable y with whole number power so this polynomial in one variable

(iii) 3√t + t√ 2

there is only one variable t but in 3√t power of t is ½ which is not a whole number so 3√t + t√ 2 is not a polynomial

(iv)y +2/y

there is only one variable y but 2/y = 2y-1 so the power is not a whole number so y +2/y is not a polynomial

(v) x10 + y3 + t50

there are three variable x y and t and there powers are whole number so this polynomial in three variable

Answer 2

Question :-

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

(i) 4x^2 – 3x + 7

(ii) y^2 + √2

(iii) 3 √t + t√2

(iv) y+ 2/y

(v) x^10+ y^3+t^50

Answer :-

(i) We have 4x^2 – 3x + 7 = 4x^2 – 3x + 7x^0

It is a polynomial in one variable i.e., x

because each exponent of x is a whole number.

(ii) We have y^2 + √2 = y^2 + √2y^0

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 √t^1/2 + √2.t

It is not a polynomial, because one of the exponents of t is 1/2,

which is not a whole number.

(iv) We have y + y+2/y = 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 x^10+  y^3 + t^50

Here, exponent of every variable is a whole number, but x^10 + y^3 + t^50 is a polynomial in x, y and t, i.e., in three variables.

So, it is not a polynomial in one variable.

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