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# NCERT Solutions, Chapter 2: Polynomials, Class 10 (Mathematics) Class 10 Notes | EduRev

## Class 10 : NCERT Solutions, Chapter 2: Polynomials, Class 10 (Mathematics) Class 10 Notes | EduRev

``` Page 1

Mathematics
(Class X)
A Free web support in education
1
Question 1:
Find the zeroes of the following quadratic polynomials and verify the
relationship between the zeroes and the coefficients.
The value of is zero when x - 4 = 0 or x + 2 = 0, i.e., when x
= 4 or x = -2
The value of 4s
2
- 4s + 1 is zero when 2s - 1 = 0, i.e., Therefore,
the zeroes of 4s
2
- 4s + 1 are  ½ and ½ .
Sum of zeroes =
The value of 6x
2
- 3 - 7x is zero when 3x + 1 = 0 or 2x - 3 = 0, i.e.,
Therefore, the zeroes of  are 4 and -2.
Sum of zeroes =
Product of zeroes
Product of zeroes
Page 2

Mathematics
(Class X)
A Free web support in education
1
Question 1:
Find the zeroes of the following quadratic polynomials and verify the
relationship between the zeroes and the coefficients.
The value of is zero when x - 4 = 0 or x + 2 = 0, i.e., when x
= 4 or x = -2
The value of 4s
2
- 4s + 1 is zero when 2s - 1 = 0, i.e., Therefore,
the zeroes of 4s
2
- 4s + 1 are  ½ and ½ .
Sum of zeroes =
The value of 6x
2
- 3 - 7x is zero when 3x + 1 = 0 or 2x - 3 = 0, i.e.,
Therefore, the zeroes of  are 4 and -2.
Sum of zeroes =
Product of zeroes
Product of zeroes
Mathematics
(Class X)
A Free web support in education
2
The value of 4u
2
+ 8u is zero when 4u = 0 or u + 2 = 0, i.e.,
u = 0 or u = -2
Therefore, the zeroes of 4u
2
+ 8u are 0 and -2.
The value of t
2
- 15 is zero when , i.e., when
or
Therefore, the zeroes of 6 x
2
- 3 - 7 x are .
Sum of zeroes =
Product of zeroes =
Sum of zeroes =
Product of zeroes =
or
Page 3

Mathematics
(Class X)
A Free web support in education
1
Question 1:
Find the zeroes of the following quadratic polynomials and verify the
relationship between the zeroes and the coefficients.
The value of is zero when x - 4 = 0 or x + 2 = 0, i.e., when x
= 4 or x = -2
The value of 4s
2
- 4s + 1 is zero when 2s - 1 = 0, i.e., Therefore,
the zeroes of 4s
2
- 4s + 1 are  ½ and ½ .
Sum of zeroes =
The value of 6x
2
- 3 - 7x is zero when 3x + 1 = 0 or 2x - 3 = 0, i.e.,
Therefore, the zeroes of  are 4 and -2.
Sum of zeroes =
Product of zeroes
Product of zeroes
Mathematics
(Class X)
A Free web support in education
2
The value of 4u
2
+ 8u is zero when 4u = 0 or u + 2 = 0, i.e.,
u = 0 or u = -2
Therefore, the zeroes of 4u
2
+ 8u are 0 and -2.
The value of t
2
- 15 is zero when , i.e., when
or
Therefore, the zeroes of 6 x
2
- 3 - 7 x are .
Sum of zeroes =
Product of zeroes =
Sum of zeroes =
Product of zeroes =
or
Mathematics
(Class X)
A Free web support in education
3
The value of 3x
2
- x - 4 is zero when 3x - 4 = 0 or x + 1 = 0, i.e.,
when or x = -1
Therefore, the zeroes of 3x
2
- x - 4 are 4/3 and -1.
Sum of zeroes =
Product of zeroes
Question 2:
Find a quadratic polynomial each with the given numbers as the sum and
product of its zeroes respectively.
Therefore, the zeroes of  t
2
- 15 are  and .
Sum of zeroes =
Product of zeroes =
Page 4

Mathematics
(Class X)
A Free web support in education
1
Question 1:
Find the zeroes of the following quadratic polynomials and verify the
relationship between the zeroes and the coefficients.
The value of is zero when x - 4 = 0 or x + 2 = 0, i.e., when x
= 4 or x = -2
The value of 4s
2
- 4s + 1 is zero when 2s - 1 = 0, i.e., Therefore,
the zeroes of 4s
2
- 4s + 1 are  ½ and ½ .
Sum of zeroes =
The value of 6x
2
- 3 - 7x is zero when 3x + 1 = 0 or 2x - 3 = 0, i.e.,
Therefore, the zeroes of  are 4 and -2.
Sum of zeroes =
Product of zeroes
Product of zeroes
Mathematics
(Class X)
A Free web support in education
2
The value of 4u
2
+ 8u is zero when 4u = 0 or u + 2 = 0, i.e.,
u = 0 or u = -2
Therefore, the zeroes of 4u
2
+ 8u are 0 and -2.
The value of t
2
- 15 is zero when , i.e., when
or
Therefore, the zeroes of 6 x
2
- 3 - 7 x are .
Sum of zeroes =
Product of zeroes =
Sum of zeroes =
Product of zeroes =
or
Mathematics
(Class X)
A Free web support in education
3
The value of 3x
2
- x - 4 is zero when 3x - 4 = 0 or x + 1 = 0, i.e.,
when or x = -1
Therefore, the zeroes of 3x
2
- x - 4 are 4/3 and -1.
Sum of zeroes =
Product of zeroes
Question 2:
Find a quadratic polynomial each with the given numbers as the sum and
product of its zeroes respectively.
Therefore, the zeroes of  t
2
- 15 are  and .
Sum of zeroes =
Product of zeroes =
Mathematics
(Class X)
A Free web support in education
4
Let the polynomial be ax
2
+ bx + c and its zeroes be ?? and ?? .
Therefore, the quadratic polynomial is 4x
2
- x - 4.
Let the polynomial be ax
2
+ bx + c and its zeroes be ?? and ?? .
Therefore, the quadratic polynomial is 3x
2
- x + 1.
Let the polynomial be ax
2
+ bx + c and its zeroes be ?? and ?? .
Therefore, the quadratic polynomial is .
Let the polynomial be ax
2
+ bx + c and its zeroes be ?? and ?? .
Page 5

Mathematics
(Class X)
A Free web support in education
1
Question 1:
Find the zeroes of the following quadratic polynomials and verify the
relationship between the zeroes and the coefficients.
The value of is zero when x - 4 = 0 or x + 2 = 0, i.e., when x
= 4 or x = -2
The value of 4s
2
- 4s + 1 is zero when 2s - 1 = 0, i.e., Therefore,
the zeroes of 4s
2
- 4s + 1 are  ½ and ½ .
Sum of zeroes =
The value of 6x
2
- 3 - 7x is zero when 3x + 1 = 0 or 2x - 3 = 0, i.e.,
Therefore, the zeroes of  are 4 and -2.
Sum of zeroes =
Product of zeroes
Product of zeroes
Mathematics
(Class X)
A Free web support in education
2
The value of 4u
2
+ 8u is zero when 4u = 0 or u + 2 = 0, i.e.,
u = 0 or u = -2
Therefore, the zeroes of 4u
2
+ 8u are 0 and -2.
The value of t
2
- 15 is zero when , i.e., when
or
Therefore, the zeroes of 6 x
2
- 3 - 7 x are .
Sum of zeroes =
Product of zeroes =
Sum of zeroes =
Product of zeroes =
or
Mathematics
(Class X)
A Free web support in education
3
The value of 3x
2
- x - 4 is zero when 3x - 4 = 0 or x + 1 = 0, i.e.,
when or x = -1
Therefore, the zeroes of 3x
2
- x - 4 are 4/3 and -1.
Sum of zeroes =
Product of zeroes
Question 2:
Find a quadratic polynomial each with the given numbers as the sum and
product of its zeroes respectively.
Therefore, the zeroes of  t
2
- 15 are  and .
Sum of zeroes =
Product of zeroes =
Mathematics
(Class X)
A Free web support in education
4
Let the polynomial be ax
2
+ bx + c and its zeroes be ?? and ?? .
Therefore, the quadratic polynomial is 4x
2
- x - 4.
Let the polynomial be ax
2
+ bx + c and its zeroes be ?? and ?? .
Therefore, the quadratic polynomial is 3x
2
- x + 1.
Let the polynomial be ax
2
+ bx + c and its zeroes be ?? and ?? .
Therefore, the quadratic polynomial is .
Let the polynomial be ax
2
+ bx + c and its zeroes be ?? and ?? .
Mathematics
(Class X)
A Free web support in education
5
Therefore, the quadratic polynomial is .
Let the polynomial be ax
2
+ bx + c and its zeroes be ?? and ?? .
Therefore, the quadratic polynomial is .
Let the polynomial be ax
2
+ bx + c and its zeroes be ?? and ?? .
Therefore, the quadratic polynomial is .
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