Question

form a quadratic polynomial if one of whose zero is 2+root 5 and sum of the zeroes is 4

Answer 1

Hi ,

Let m , n are two zeroes of the quadratic

polynomial ,

It is given that m = 2 + √5 ---( 1 )

m + n = 4 ---( 2 )

substitute m value in equation ( 2 ) , we get

2 + √5 + n = 4

n = 4 - 2 - √5

n = 2 - √5

Therefore ,

second zero = n = 2 - √5

product if the zeroes =

mn = ( 2 + √5 ) ( 2 - √5 )

mn = 2² - ( √5 )²

mn = 4 - 5

mn = -1 ----( 3 )

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We know the ,

form of quadratic polynomial whose zeroes

are m , n is

x² - ( m + n )x + mn

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from ( 2 ) and ( 3 ) ,

Required polynomial is

x² - 4x - 1

I hope this helps you.

: )

Answer 2

Hiii friend,


Let Alpha and beta are the zeros of the polynomial P(X).


Let Alpha = 2+✓5


Sum of zeros = 4

Alpha + Beta = 4

2+✓5 + Beta = 4

Beta = 4-2-✓5 => 2-✓5



Therefore,

Sum of zeros = (Alpha + Beta) = (2+✓5 + 2-✓5) = 4

and,

Product of zeros = (Alpha × Beta) = (2+✓5)(2-✓5) = (2)² - (✓5)² = 4-5 = -1


Therefore,


Required Quadratic polynomial = X²-(Alpha + Beta)X + Alpha × Beta

=> X²-(4)X+(-1)


=> X²-4X-1


HOPE IT WILL HELP YOU..... :-)