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Find a quadratic polynomial whose zeroes are 3+root 5 & 3-root5

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Given -> 3 -  √5 and 3 +  √5 are zeros of a polynomial

let p(x) be required polynomial

====> x - (3 + √5) and x - (3 - √5) are factors of p(x)

====> [x - (3 + √5)] [x - (3 - √5) is required polynomial

= [x - 3 - √5] [x - 3 + √5]

= x2 - 3x + √5x - 3x + 9 - 3√5 - √5x + 3√5 - 5

= x2 - 6x + 4

This is the required polynomial

Hope this helps!!

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Thank you so much :*

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yes
 
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the mutiplication is wrong
 
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Utkakrsh Singh is Right
 
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If alpha and bita are the zeros of quadratic polynomial 2xsquare-4x+b,if 2alpha and 3bita=8

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zeroes = 3+root5 and 3-root5

product of zeroes= (3+root5)(3-root5) 
                           = 9-5
                           =4

sum of zeroes=3+root5 + 3-root5
                      =6


we know p(x) = k(x2^ - sum of zeroes (x) + product of zeroes
                       = k(x2^ -6x +4)

hope it helps

 
  • 3

Given -> 3 -  √5 and 3 +  √5 are zeros of a polynomial

let p(x) be required polynomial

====> x - (3 + √5) and x - (3 - √5) are factors of p(x)

====> [x - (3 + √5)] [x - (3 - √5) is required polynomial

= [x - 3 - √5] [x - 3 + √5]

= x2 - 3x + √5x - 3x + 9 - 3√5 - √5x + 3√5 - 5

= x2 - 6x + 4

This is the required polynomial

Hope this helps!!

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