MP Board Class 9th Maths Solutions Chapter 2 Polynomials Ex 2.1

MP Board Class 9th Maths Solutions Chapter 2 Polynomials Ex 2.1

Question 1.
Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

  1. 4x2 – 3x + 7
  2. y2 + √2
  3. 3√t + t√2
  4. y + \(\frac{2}{y}\)
  5. x10 + y3 + t50.

Solution:
1. 4x2 – 3x + 7
This expression is a polynomial in one variable .r because in the expression there is only one variable (x) and all the indices of x are whole numbers.

2. y2 + √2
This expression is a polynomial in one variable y because in the expression there is only one variable (y) and all the indices of y are whole numbers.

3. 3√t + t√2
This expression is not a polynomial because in the term 3√t, the exponent of t is \(\frac{1}{2}\), which is not a whole number.

4. y + \(\frac{2}{y}\)
This expression is not a polynomial because in the term \(\frac{2}{y}\) the exponent of y is (-1) which is not a whole number.

5. x10 + y3 + t50
This expression is not a polynomial in one variable because in the expression, three variables (x, y and t) occur.

Question 2.
Write the coefficients of x2 in each of the following:

  1. 2 + x2 + x
  2. 2 – x2 + x3
  3. \(\frac{π}{2}\)x2 + x
  4. \(\sqrt{2x}\) – 1

Solution:
1. 2 + x2 + x
Coefficient of x2 = 1

2. 2 – x2 + x3
Coefficient of x2 = – 1

3. \(\frac{π}{2}\)x2 + x
Coefficient of x2 = \(\frac{π}{2}\)

4. \(\sqrt{2x}\) – 1
Coefficient of x2 = 0.

Question 3.
Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Solution:
One example of a binomial of degree 35 is 3x35 – 4.
One example of a monomial of degree 100 is √2y100

Question 4.
Write the degree of each of the following polynomials:

  1. 5x3 + 4x2 + 7x
  2. 4 – y2
  3. 5x3 – √7
  4. 3

Solution:
1. 5x3 + 4x2 + 7x
Term with the highest power of x = 5x3
Exponent of x in this term = 3
∴ Degree of this polynomial = 3.

2. 4 – y2
Term with the highest power of y = – y2
Exponent of y in this term = 2
∴ Degree of this polynomial = 2.

3. 5t – √7
Term with the highest power of t = 5t
Exponent of t in this term = 1
∴ Degree of this polynomial = 1.

4. 3
It is a non-zero constant. So the degree of this polynomial is zero.

Question 5.
Classify the following as linear, quadratic and cubic polynomials:

  1. x2 + x
  2. x – x3
  3. y + y2 + 4
  4. 1 + x
  5. 3t
  6. r2
  7. 7x3

Solution:

  1. Quadratic
  2. Cubic
  3. Quadratic
  4. Linear
  5. Linear
  6. Quadratic
  7. Cubic.

Zero’s of a Polynomial:
1. A zero of a polynomial p(x) is a number c such that p(c) = 0. Here p(x) = 0 is a polynomial equation and c is the root of the polynomial equation.

2. A non-zero constant polynomial has no zero. Every real number is a zero of the zero polynomial.

Some Observations:

  1. A zero of a polynomial need not be 0.
  2. 0 may be a zero of a polynomial.
  3. Every linear polynomial has one and only one zero.
  4. A polynomial can have more than one zero.

MP Board Class 9th Maths Solutions

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