Polynomials — Class 10 Mathematics
Mathematics · Chapter 2
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Chapter summary
Key ideas & terms
- Polynomial
- An expression with non-negative integer powers of the variable.
- Zero of a polynomial
- A value of the variable for which the polynomial equals zero.
- Degree
- The highest power of the variable in the polynomial.
- Sum/product of zeroes
- For
: sum , product .
Extra questions & answers
Find the sum and product of the zeroes of
Sum
What is the geometrical meaning of the zeroes of a polynomial?
They are the x-coordinates of the points where the graph of the polynomial intersects the x-axis.
What is the degree of a polynomial? Give the degree of a linear, quadratic and cubic polynomial.
The highest power of the variable in the polynomial; linear has degree 1, quadratic degree 2 and cubic degree 3.
What is the geometrical meaning of the zeroes of a polynomial?
They are the x-coordinates of the points where the graph of the polynomial cuts or touches the x-axis (refer to the graphs in your NCERT textbook).
For a quadratic polynomial
Sum of the zeroes
Find the zeroes of
Form a quadratic polynomial whose zeroes are 3 and
Sum
How many zeroes can a quadratic and a cubic polynomial have at most?
A quadratic polynomial has at most 2 zeroes and a cubic polynomial has at most 3 zeroes (equal to its degree).
If one zero of
Substituting
Write the relationship between the zeroes and coefficients of a cubic polynomial
Sum of zeroes
EXERCISE 2.1
1. The graphs of
The number of zeroes equals the number of points at which the graph intersects the
EXERCISE 2.2
1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (i)
Factorising,
1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (ii)
Factorising,
1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (iii)
Rearranging and factorising,
1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (iv)
Factorising,
1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (v)
Using the difference of squares,
1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (vi)
Factorising,
2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (i)
For sum
2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (ii)
Using
2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (iii)
Using
2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (iv)
Using
2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (v)
Using
2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (vi)
Using