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

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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.

Given a polynomial function, identify the degree and leading coefficient calculator…. the following exercises, graph the polynomial functions using a calculator.

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.

Square polynomial root calculator. grade 10 math linear algebra substitution word problems.

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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