Question

find a a quadratic polynomial whose Zeros are
5- 3
$\sqrt{2}$
and 5+ 3/2​

Answer 1

Correct Question :-)

Find the quadratic polynomial whose zeros are 5 - 3√2 and 5 + 3√2.

Solution:-)

$Let \: Sum \: of \: zeros = s \\ \\ s =( 5 - 3 \sqrt{2} ) + (5 + 3 \sqrt{2} ) \\ \\ s = 5 - \cancel{ 3\sqrt{2}} + 5 + \cancel{ 3\sqrt{2} } \\ \\ \purple{\Large{\boxed{\boxed{s = 10}}}}$

$Let \: Product \: of \: zeros = p \\ \\ p = (5 - 3 \sqrt{2} )(5 + 3 \sqrt{2} ) \\ \\ p = {5}^{2} - ( {3 \sqrt{2} )}^{2} \\ \\ p = 25 - 18 \\ \\ \purple{\Large{\boxed{\boxed{p = 7}}}}$

As quadratic polynomial having sum of zeros s and product of zeros p is of the form

$a {x}^{2} - sx + p$

So reqrd polynomial is

$\purple{\Large{\boxed{\boxed{ {x}^{2} - 10x + 7 }}}}$