# NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.2

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.2 are part ofÂ NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.2.

• Polynomials Class 10 Ex 2.1
• Polynomials Class 10 Ex 2.2
• Polynomials Class 10 Ex 2.3
• Polynomials Class 10 Ex 2.4

## NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.2

Ex 2.2 Class 10 Maths Question 1.
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and their coefficients:
(i)Â x2Â â€“ 2x â€“ 8
(ii)Â 4s2Â â€“ 4s + 1
(iii)Â 6x2Â â€“ 3 â€“ 7x
(iv)Â 4u2Â + 8u
(v)Â t2Â â€“ 15
(vi)Â 3x2Â â€“ x â€“ 4
Solution:
(i)
Â x2Â â€“ 2x â€“ 8 = x2Â â€“ 4x + 2x â€“ 8
= x(x â€“ 4) + 2(x â€“ 4)
= (x + 2) (x â€“ 4)
Either x + 2 = 0 or x â€“ 4 = 0
â‡’Â  x = -2 or x = 4
Hence, zeroes of this polynomial are -2 and 4.
Verification:
Sum of the zeroes = (-2) + (4) = 2
=Â $\frac { (-2) }{ 1 }$Â =Â $\frac { -b }{ a }$
Product of zeroes = (-2) (4) = -8 = Â $\frac { -8 }{ 1 }$
=Â Â $\frac { c }{ a }$
Hence verified.

(ii)Â 4s2Â â€“ 4s + 1 = (2s â€“ l)2Â = (2s â€“ l)(2s â€“ 1)
Either 2s â€“ 1 = 0 orÂ 2s â€“ 1 = 0
i.e. , s =Â Â $\frac { 1 }{ 2 }$Â ,Â $\frac { 1 }{ 2 }$
Hence, the two Zeroes areÂ $\frac { 1 }{ 2 }$Â andÂ $\frac { 1 }{ 2 }$
Verification:

Hence verified.

(iii)Â 6x2Â â€“ 3 â€“ 7x = 6x2Â â€“ 7x â€“ 3
= 6x2Â â€“ 9x + 2x â€“ 3
= 3x (2x â€“ 3) + 1(2x â€“ 3)
= (2x â€“ 3) (3x + 1)
Either 2x â€“ 3 = 0 or 3x+1 = 0

Hence verified.

(iv) 4u2 + 8u  â‡’  4u(u + 2)
Either 4u = 0 or u + 2 = 0
â‡’ u = 0 or u = -2
Hence, the two zeroes are 0 and -2.
Verification:
Sum of the zeroes = 0 + (-2) = -2
$\frac { -8 }{ 4 }$ = $\frac { -b }{ a }$
Product of zeroes = 0 x (-2) = 0 =  $\frac { c }{ a }$
Hence verified.

(v) t2 â€“ 15 = t2 â€“ ($\sqrt{15}$)2
= (t + ($\sqrt{15}$) (t- ($\sqrt{15}$)
Either t + ($\sqrt{15}$ = 0 or t â€“ ($\sqrt{15}$ = 0
â‡’ t = -($\sqrt{15}$ or t = ($\sqrt{15}$
Hence, the two zeroes are -($\sqrt{15}$ and + $\sqrt{15}$.
Verification:
Sum of the zeroes = -($\sqrt{15}$ + $\sqrt{15}$ = 0
$\frac { -b }{ a }$
Product of zeroes = â€“$\sqrt{15}$ x $\sqrt{15}$ = -15
$\frac { c }{ a }$
Hence verified.

(vi) 3x2 â€“ x â€“ 4 = 3x2 â€“ 4x + 3x â€“ 4
=  x(3x â€“ 4) + l(3x 4)
= (x + 1) (3x â€“ 4)
Either x + 1 = 0 or 3x-4 = 0
â‡’  x = -1 or x =  $\frac { 4 }{ 3 }$
Verification:
Sum of the zeroes = -1 + $\frac { 4 }{ 3 }$ =  $\frac { 1 }{ 3 }$ =  $\frac { -b }{ a }$
Product of zeroes = -1 x $\frac { 4 }{ 3 }$ =  $\frac { -4 }{ 3 }$ =  $\frac { c }{ a }$
Hence verified.

Ex 2.2 Class 10 Maths Question 2.
Find a quadratic polynomial each with the given numbers as the sum and product of zeroes respectively:

Solution:
(i) Let the zeroes of polynomial be Î± and Î².
Then, Î± + Î² = $\frac { 1 }{ 4 }$ and Î±Î² = -1
âˆ´ Required polynomial is given by,
x2 â€“ (Î± + Î²)x + Î±Î² = x2 â€“ $\frac { 1 }{ 4 }$x + (-1)
= x2 â€“ $\frac { 1 }{ 4 }$x â€“ 1
= 4x2 â€“ x â€“ 4

(ii) Let the zeroes of polynomial be Î± and Î².
Then, Î± + Î²= âˆš2 and Î±Î² = $\frac { 1 }{ 3 }$
âˆ´  Required polynomial is:
x2 â€“ (Î± + Î²)x + Î±Î² = x2 â€“ âˆš2x + $\frac { 1 }{ 3 }$
= 3x2 â€“ 3âˆš2x + 1

(iii) Let the zeroes of the polynomial be Î± and Î².
Then, Î± + Î² = 0 and Î±Î² = âˆš5
âˆ´ Required polynomial
= x2 â€“ (Î± + Î²)x + Î±Î²
= x2â€“ 0 x x + âˆš5 = x2 + âˆš5

(iv) Let the zeroes of the polynomial be Î± and Î².
Then, Î± + Î² = 1 and Î±Î² = 1.
âˆ´  Required polynomial
= x2 â€“ (Î± + Î²)x + Î±Î²
= x2 â€“ x + 1

(v) Let the zeroes of the polynomial be Î± and Î².
Then, Î± + Î² = â€“ $\frac { 1 }{ 4 }$ and Î±Î² = $\frac { 1 }{ 4 }$
âˆ´ Required polynomial
= x2 â€“ (Î± + Î²)x + Î±Î²
= x2 â€“ (- $\frac { 1 }{ 4 }$ ) + $\frac { 1 }{ 4 }$
=  4x2 + x + 1 = 0

(vi) Let the zeroes of the polynomial be Î± and Î².
Then, Î± + Î² = 4 and Î±Î² = 1.
âˆ´ Required polynomial = x2 -(Î± + Î²)x + Î±Î²
= x2 â€“ 4x + 1

We hope the NCERT Solutions for Class 10 Mathematics Chapter 2 Polynomials Ex 2.2 help you. If you have any query regarding NCERT Solutions for Class 10 Mathematics Chapter 2 Polynomials Ex 2.2 drop a comment below and we will get back to you at the earliest.

âœ¨Join SocialMe, a platform created by Success Router to discuss problem and share knowledge