Question

ᑎO Տᑭᗩᗰ❌❌

write a quadratic polynomial whose zeroes are
$3 + \sqrt{2} \: and \: 3 - \sqrt{2}$
​

Answer 1

$\huge{\underbrace{\bf{\bold{\pink{Question:}}}}}$

Write a quadratic polynomial whose zeroes are 3+√2 and 3-√2.

$\huge{\underbrace{\bf{\bold{\pink{Answer:}}}}}$

x² - 6x +7

$\huge{\underbrace{\bf{\bold{\pink{Explaination:}}}}}$

Zeroes of a polynomial represents its roots.

Let,

$\alpha = 3 + \sqrt{2} \\ \beta = 3 - \sqrt{2}$

Sum of the roots = α + β

=> 3+√2 + (3-√2)

=> 3+√2+3-√2

=> 6

Product of the roots = α × β

=> 3+√2 × (3-√2)

=> (3)² - (√2)²

=> 9 - 2

=> 7

We know a polynomial can be written as :

x² - (α + β)x + (α × β)

So, substitute the values as follows :

=> x² - (6)x + (7)

=> x² - 6x + 7

Hope it helps you !!

✌️

Answer 2

Answer:

X2 - 6x + 7 is the answer.....

Hope it helps...⚡