Question

The quadratic polynomial whose zeroes are
$5 + \sqrt{2}$
and
$5 - \sqrt{2}$
is​

Answer 1

REFER TO THE ATTACHMENT FOR THE ANSWER

Answer 2

Step-by-step explanation:

Let the zeroes be α and β respectively.

i.e.,

$\alpha = 5 + \sqrt{2} \\ \beta = 5 - \sqrt{2}$

Then,,

$\alpha + \beta = 5 + \sqrt[]{2} + 5 - \sqrt{2} = 10 \\ \\ \alpha \times{ \beta } = (5 + \sqrt{2} ) (5 - \sqrt{2} ) = 25-2=23$

Using Formula,,

$ax {}^{2} + bx + c = {x}^{2} - (a + \beta )x + \alpha \beta$

$a {x}^{2} + bx + c \\ = {x}^{2} - (10)x + 2 \sqrt{2} \\ = {x}^{2} - 10x + 23$

Therefore,, The quadratic polynomial is,

x²-10x+23

Hope it helps ❣️❣️❣️