Question

form quadratic polynomial whose zeroes 7+√5 and 7-√5​

Answer 1

$x = 7 + \sqrt{5}$

$x = 7 - \sqrt{5}$

${x - 7 - \sqrt{5}} \: and \: x - 7 + \sqrt{5}$

$(x - 7 - \sqrt{5})(x - 7 + \sqrt{5})$

$(x - 7) {}^{2} - 5$

$x {}^{2} + 49 - 14x - 5$

$x {}^{2} - 14x + 44$

Answer 2

$\huge\underline\mathfrak\pink{Answer-}$

x² - 14x + 44

$\huge\underline\mathfrak\pink{Explanation-}$

Given zeroes : 7 + √5 ; 7 - √5

To form : Quadratic polynomial.

Solution :

Firstly, we have to find 'sum of zeroes'

➮ Sum of zeroes = 7 + √5 + 7 - √5

Cancelling the negative and positive √5.

➮ Sum of zeroes = 7 + 7

➮ Sum of zeroes = 14

Now, we have to find 'product of zeroes'

➮ Product of zeroes = ( 7 + √5 ) ( 7 - √5 )

We know that,

( a + b ) ( a - b ) = a² - b²

➮ Product of zeroes = (7)² - (√5)²

➮ Product of zeroes = 49 - 5

➮ Product of zeroes = 44

_________________

$\bold\blue{Formula\:to\:form\:quadratic\:polynomial-}$

➮ x² - Sx + P

where, S refers to sum of zeroes.

and P refers to product of zeroes.

➮ x² - 14x + 44 ( required Quadratic polynomial )