Question

Find a quadratic polynomial whose zeroes are 5+ _|2 and 5-_|2

Answer 1

Heya friend ☺

Here is your answer

Let α=5+√2 and β=5-√2

SUM OF ZEROES :

=α+β

=5+√2+5-√2

=10

PRODUCT OF ZEROES :

=αβ

=(5+√2)(5-√2)

=(5)²-(√2)²

=25-2

=23

POLYNOMIAL :

=x²-(sum of zeroes)x +product of zeroes

=x²-10x+23

HOPE THIS HELPS YOU

Answer 2

Hey dear !!!

___________________________

==> In the example,

We have given that 5+√2 and 5-√2 are the zeroes of the quadratic polynomial.

We have to find the quadratic polynomial.

Let ,

α and β are the two zeroes of the polynomial .

hence,

α = 5+√3 and β = 5-√2

We know that,

Sum of zeroes = α + β

= 5+√2 + 5-√2

= 5+5 (√2 -√2)

= 10

∴ α + β = 10

Also we know,

Product of zeroes = αβ

= 5+√2 *5-√2

= 5*5 (√2*(-√2)

= 25 - 2

= 23

∴ αβ = 23

Required quadratic polynomial is,

=> x²- (α +β)x + αβ

=> x² - 10x + 23


Therefore, x² - 10x + 23 is the required polynomial which fit in the given data.

Thanks !!!

[Be Brainly ]