Question

a quadratic polynomial whose zeroes are root 2 and root 6/2 are {where, k is a non zero constant]

a - k(x^2-(2+root3)x + root6)
b - k(root2x^2+ (2+root3)x + root6)
c - k(root2x^2-(2+root3)x+root6)
d - k(x^2-(2+root3)x-root6)

ill mark brainliest to someone who answers with correct explaination

Answer 1

Answer:

I hope this answer will help you

Answer 2

Given :  a quadratic polynomial whose zeroes are √2 and √6/2 are  \ k is a non zero constant  

To Find :  quadratic polynomial

a   k(x²-(2+√3)x + √6)

b   k(√2x²+ (2+√3)x + √6)

c   k(√2x²-(2+√3)x+√6)

d   k(x²-(2+√3)x-√6)

Solution:

a quadratic polynomial whose zeroes are  α and β

can be written as

k ( x²  - (sum of zeroes)x  + product of zeroes)  where k ≠ 0

k ( x²  - (α + β )x  + αβ)  

Here zeroes are √2 and √6/2

sum of zeroes =  √2  + √6/2   =     (1/√2)( 2  + √3 )  

Product of zeroes  =  √2 * √6/2   =  √12 / 2 =  √3

sum of zeroes =   (1/√2)( 2  + √3 )  

Product of zeroes  =  √3

polynomial

= k ( x²  -(1/√2)( 2  + √3 ) x  + √3)  

Taking 1/√2 common

= (k / √2 )( √2x²  - ( 2  + √3 ) x  + √6)  

= k ( √2x²  - ( 2  + √3 ) x  + √6)       k and k/√2 are same as k is any non zero constant

k ( √2x²  - ( 2  + √3 ) x  + √6)  

k(√2x²-(2+√3)x+√6) is correct option

Quadratic polynomial is k(√2x²-(2+√3)x+√6)

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