Question

Find the quadratic polynomial vhose zeroes are 5+√2 and 5 -√2​

Answer 1

Answer:

5+√2 = α

5-√2 = β

α+β=5+√2+5-√2

=10

αβ=(5+√2)(5-√2)

= 5²-√2²

25-2

=23

x²-10x+23

Answer 2

Answer:

For making quadratic polynomial we can apply this formulae. x^2-(sum of zeroes)x+(product of zeroes) =0

two of its zeroes are 5+√2 and 5-√2

therefore,

α=5+√2 and β=5-√2

sum of zeroes=(5+√2)+(5-√2)

=10

product of zeroes=(5+√2)(5-√2)

=25-5√2+5√2-√4

=25-2

=23

then the quadratic equation is x^2-10x-23=0