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
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1 
Question 1:  
Find the zeroes of the following quadratic polynomials and verify the 
relationship between the zeroes and the coefficients.  
Answer 1:  
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
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(Class X) 
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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.  
Answer 1:  
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
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(Class X) 
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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
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(Class X) 
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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.  
Answer 1:  
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
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(Class X) 
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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
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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.  
Answer 2:  
Therefore, the zeroes of  t 
2 
- 15 are  and .  
Sum of zeroes = 
Product of zeroes =  
Page 4


Mathematics
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(Class X) 
www.tiwariacademy.com 
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.  
Answer 1:  
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
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(Class X) 
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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
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(Class X) 
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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.  
Answer 2:  
Therefore, the zeroes of  t 
2 
- 15 are  and .  
Sum of zeroes = 
Product of zeroes =  
Mathematics
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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
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(Class X) 
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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.  
Answer 1:  
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
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(Class X) 
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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
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(Class X) 
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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.  
Answer 2:  
Therefore, the zeroes of  t 
2 
- 15 are  and .  
Sum of zeroes = 
Product of zeroes =  
Mathematics
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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
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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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