Question

Form the polynomial whose zeroes are 4+√2/2 and 4-√2/2.
ANSWER IT ASAP

Answer 1

Let a and b are the zeroes of the polynomial.

a = 4+√2/2 and b = 4-√2/2

Sum of zeroes = 4+√2/2+4-√2/2

→ a+b = 8

Product of zeroes = (4+√2/2)(4-√2/2)

→ = (4²-(√2/2)²)

→ = 16-2/4

→ = 16-1/2

→ ab = 31/2

Required polynomial = k{x²-(a+b)x+ab}

→ k{x²-8x+31/2}

Put k = 2

→ 2x²-16x+31

Hope it helps…

Answer 2

Let α and β are the zeroes of the polynomial.

α = 4+√2/2
 β = 4-√2/2

Sum of zeroes [ α + β ] 
               = 4 + √2/2 + 4 - √2/2
               =  8

Product of zeroes [ αβ ]
            = (4+√2/2)(4-√2/2)

             =  4² -  (√2/2)² 

              = 16 -2/4

              = 16 -1/2
             
             = 31/2


Quadratic polynomial :- 
     = k[x²-(α+ β)x+αβ]

     k[x²-8x+31/2 ] 

k = 2,

2[x²-8x+31/2 ] 

== 2x²-16x+31  ----> required polynomial