Chapter 02 Polynomials 

Problem No 01 :- Find the Zeros of the Polynomials and verify the relationship between the zeros and coefficients :-

x² + 7x + 12

To find the zeros of polynomial, It should be equated to zero first

Hence,

x² + 7x + 12 = 0

Or, x² + 4x + 3x + 12 = 0

Or, x (x + 4)+ 3 (x + 4 ) = 0

Or, (x + 3) * (x + 4 ) = 0

It implies that x = - 3 & -4 Ans ............................................... (1)

Comparing the Given Eqn with Stnd Eqn i.e. ax² + bx + c = 0

We Get, a=1 , b = 7 & c = 12

α + β = -3 + ( - 4) = - 7................................... (2)

-b /a = -7 / 1 = -7 .............................................(3)

Also α * β = -3 * -4 = 12 .................................(4)

c / a = 12 / 1 ......................................................(5)

From (2), (3) (4) & (5) relation between the zeros and coefficients can be verified.

Problem No 02 :- Find the Zeros of the Polynomials and verify the relationship between the zeros and coefficients :-

x² - 2x - 8

To find the zeros of polynomial, It should be equated to zero first

Hence,

x² - 2x – 8

Or, x² - 4x + 2x – 8 = 0

Or, x (x - 4)+ 2 (x - 4 ) = 0

Or, (x + 2) * (x - 4 ) = 0

It implies that x = - 2 & 4 Ans ............................................... (1)

Comparing the Given Eqn with Stnd Eqn i.e. ax² + bx + c = 0

We Get, a=1 , b = -2 & c = -8

α + β = - 2 + ( 4) = 2........................................... (2)

-b /a = -(-2) / 1 = 2 ..................................................(3)

Also α * β = -2 * 4 = -8 ..........................................(4)

c / a = -8 / 1 = -8 ......................................................(5)

From (2), (3) (4) & (5) relation between the zeros and coefficients can be verified.

Problem No 03 :- Find the Zeros of the Polynomials and verify the relationship between the zeros and coefficients :-

x² + 3x - 10

To find the zeros of polynomial, It should be equated to zero first

Hence,

x² + 3x – 10 = 0

Or, x² + 5x - 2x – 10 = 0

Or, x (x + 5) - 2 (x + 5 ) = 0

Or, (x - 2) * (x + 5 ) = 0

It implies that x = 2 & - 5 Ans ............................................... (1)

Comparing the Given Eqn with Stnd Eqn i.e. ax² + bx + c = 0

We Get, a=1 , b = 3 & c = -10

α + β = 2 + ( - 5) = -3........................................... (2)

-b /a = -(3) / 1 = -3 ..................................................(3)

Also α * β = 2 * -5 = -10 ..........................................(4)

c / a = -10 / 1 = -10 ......................................................(5)

From (2), (3) (4) & (5) relation between the zeros and coefficients can be verified.

CBSE 2008C

Problem No 04 :- Find the Zeros of the Polynomials and verify the relationship between the zeros and coefficients :-

4x² - 4x - 3

To find the zeros of polynomial, It should be equated to zero first

Hence,

4x² - 4x - 3 = 0

Or, 4x² - 6x + 2x – 3 = 0

Or, 2x (2x - 3 ) + 1 (2x - 3 ) = 0

Or, (2x + 1) * (2x - 3 ) = 0

It implies that x = -1/2 & 3/2 Ans ............................................... (1)

Comparing the Given Eqn with Stnd Eqn i.e. ax² + bx + c = 0

We Get, a=4 , b = -4 & c = - 3

α + β = -1/2 + (3/2) = 1........................................... (2)

-b /a = -(-4) / 4 = 1 ..................................................(3)

Also α * β = -1/2 * 3/2 = -3/4 ..........................................(4)

c / a = -3 / 4 = -3/4 ......................................................(5)

From (2), (3) (4) & (5) relation between the zeros and coefficients can be verified.

CBSE 2008

Problem No 05 :- Find the Zeros of the Polynomials and verify the relationship between the zeros and coefficients :-

5x² - 8x - 4

To find the zeros of polynomial, It should be equated to zero first

Hence,

5x² - 8x - 4 = 0

Or, 5x² - 10x + 2x – 4 = 0

Or, 5x (x - 2 ) + 2 (x - 2 ) = 0

Or, (5x + 2) * (x - 2 ) = 0

It implies that x = -2/5 & 2 Ans ............................................... (1)

Comparing the Given Eqn with Stnd Eqn i.e. ax² + bx + c = 0

We Get, a=5 , b = -8 & c = - 4

α + β = -2/5 + (2) = 8/5 ........................................... (2)

-b /a = -(-8) / 5 = 8/5 ..................................................(3)

Also α * β = -2/5 * 2 = -4/5 ..........................................(4)

c / a = -4 / 5 = -4/5 ......................................................(5)

From (2), (3) (4) & (5) relation between the zeros and coefficients can be verified.

To read More Such Posts related to Class 10 Click on the Links Given Below :- 

• Misc Questions/ Answers Submitted by Students

• Chapter-wise Study Material For Class 10 Maths

• Important Questions related to Polynomials 

• Click Here to submit your Questions and Queries.