Question

a)find the quadratic polynomial whose zeroes are 2+√3 and 2-√3

b)find the quadratic polynomial whose zeroes are 7+2√2 and 7-2√2
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Answer 1

a) Zeroes are 2 + √3 and 2 - √3

[x - (2 + √3)] [x - (2 - √3)]

= (x - 2 - √3) (x - 2 + √3)

= x^2 - 2x - √3x - 2x + 4 + 2√3 + √3x - 2√3 - 3

= x^2 - 4x + 1

b) Zeroes are 7 + 2√2 and 7 - 2√2

[x - ( 7 + 2√2 )] [x - ( 7 - 2√2 )]

= (x- 7 - 2√2 ) ( x- 7 + 2√2 )

= x^2 - 7x + 2√2x - 7x + 49 - 14√2 - 2√2x + 14√2 - 8

= x^2 - 14x + 41

Answer 2

a ) First Zeros = 2 + √3

Second Zeros = 2 - √3

• Sum of Zeros

2 + √3 + 2 - √3

= 4

• Product of Zeros

( 2 + √3 ) ( 2 - √3 )

[ Using identity ( a + b ) ( a - b ) = a² - b² ]

4 - 3 = 1


✴ To find the Quadratic equation When Sum and product of Zeros are known is :-

x² - ( Sum of Zeros )x + Product of Zeros

So , Here

Required Quadratic equation is

x² - 4x + 1


b ) First Zeros = 7 + 2√2

Second Zeros = 7 - 2√2

• Sum of Zeros

7 + 2√2 + 7 - 2√2

= 14

• Product of Zeros

( 7 + 2√2 ) ( 7 - 2√2 )

= 49 - 8

= 41

Required Quadratic equation is :-

x² - 14x + 41