Polynomials – Exercise 2.1 – (MATHEMATICS) – 9th Class

Exercise 2.1

 

1.  Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
(i) 4x² = 3x + 7

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Ans.- 4{x^2} - 3x + 7 is a polynomial in variable x, as exponents of the variable in different terms are whole numbers.

(ii) y² + \sqrt 2

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Ans.- {y^2} + \sqrt 2 is a polynomial in variable y, as exponent of variable y is a whole number.

(iii) 3\sqrt t + t\sqrt 2

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Ans.- 3\sqrt t + t\sqrt 2 = 3{t^{{1 \over 2}}} + \sqrt 2 t is not a polynomial, as exponent of variable t in first term, i.e., 3 t 1/2 is not a whole number.

(iv) y + {2 \over y}

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Ans.- y + {2 \over y} = y + 2{y^{ - 1}} is not a polynomial, as exponent of the variable y in the term 2y-1  is not a whole number.

(v) {x^{10}} + {y^3} + {t^{50}}

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Ans.-  x10 + y3 + t50 is a polynomial in three variables.

2. Write the coefficient of x2 in each of the following :
(i) 2 + x2 + x

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Ans. –   Coefficient of x² in 2 + x² + x is 1 .

(ii) 2 – x2 + x3

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Ans. –  Coefficient of x² in 2 – x² + x³ is – 1.

(iii) {\pi \over 2}{x^2} + x

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Ans. –  Coefficient of x² in {\pi \over 2}{x^2} + x  is {\pi \over 2}

(iv)  \sqrt 2 x - 1

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Ans. – Coefficient of x² in \sqrt 2 – 1 is 0.

3. Give one example each of a binomial of degree 35, and of a monomial of degree 100.

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Sol.
(i) Binomial of degree 35 is 2×35 + x.
(ii) Monomial of degree 100 is – 7×100

4. Write the degree of each of the following polynomials:
(i) 5×3 + 4×2 + 7x

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Ans. – Degree of polynomial  5{x^3} + 4{x^2} + 7x is 3.

(ii) 4 – y2

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Ans. – Degree of polynomial 4 – y2 is 2.

(iii) 5t – \sqrt 7

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Ans. – Degree of polynomial 5t – \sqrt 7  is 1.

(iv)

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Ans. – Degree of polynomial 3 is o.

5. Classify the following as linear, quadratic and cubic polynomials :
(i) x2 + x

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Ans. –  Polynomial x2 +x ia a quadratic polynomial.

(ii) x-x3

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Ans. – Polynomial x – x³ is a cubic polynomial.

(iii) y + y2+4

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Ans. – Polynomial  y + y² + 4  is a quadratic polynomial.

(iv)  1 + x

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Ans. – Polynomial 1 + x is a linear polynomial.

(v) 3t

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Ans. – Polynomial 3t is a linear polynomial.

(vi) r2

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Ans. – Polynomial r2 is a quadratic polynomial.

(vii) 7×3

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Ans. – Polynomial 7×3  is a cubic polynomial.

 


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