Question

Find a quadratic polynomial whose zeroes are 5+root2 and 5-root2

Answer 1

Given zeroes,
5+√2 and 5-√2
Sum of the zeroes=5+√2+5-√2
Sum of the zeroes=10
Product of zeroes=(5+√2)(5-√2)
Product of zeroes=25-2=23
We know that quadratic polynomial is in the form of,
=k{x²-(sum of zeroes)x+product of zeroes}
By putting required values we get,
=k{x²-10x+23}

=x²-10x+23

Hence x²-10x+23 is the required polynomial.

Answer 2

Roots are (5+√2) (5-√2)

(x- 5-√2) ( x - 5+√2)

x² +(√2-5) x -x (5+√2)
+(25-2)
x²+x( √2-5 -5 -√2) +23

x² - 10x +23