Question

एक द्विघात बहुपद ज्ञात कीजिए जिसके soonyak 3प्लस रूट 2 तथा 3 - रूट 2 है

Answer 1

Thanks for the question!

We are required to find a quadratic polynomial whose roots are 3 + √2 , 3 - √2 .

As we know, Quadratic polynomial with roots α , β =
$k( {x}^{2} - ( \alpha + \beta )x + \alpha \beta )$

Here α = 3 +√2
β = 3 - √2

Now,
Quadratic polynomial = k [ x² - ( 3+√2+3-√2)x + (3+√2)(3-√2) ]

= k [ x² - 6x + (9-2) ]

= k ( x² - 6x + 7 )

= x² - 6x + 7 ( Taken k = 1 )

Therefore, The quadratic polynomial whose zeroes are 3 + √2 , 3 - √2 is x² - 6x + 7

इसलिए, द्विघात बहुपद जिनके शून्य 3 + √2 हैं, 3 - √2 x² - 6x + 7 है