Question

The quadratic equation whose one rational root is 3 + √2 is *
1 point
*​

Answer 1

Question -

$Find \: the \: quadratic \: equation \: whose \: one \\ rational \: root \: is \: 3 + \sqrt{2}$

Solution -

$For \: the \: quadratic \: equation \\ if \: one \: root \: is \: 3 + \sqrt{2}$

$Other \: roots = 3 - \sqrt{2}$

$Sum \: of \: roots = 3 + \sqrt{2} + 3 - \sqrt{2}$

$Sum \: of \: roots = 6$

And,

$Product \: of \: roots = (3 + \sqrt{2} )(3 - \sqrt{2} )$

$Product \: of \: roots = {(3)}^{2} - {( \sqrt{2} })^{2}$

$Product \: of \: roots = 9 - 2$

$Product \: of \: roots = 7$

We know that,

Quadratic equation=x²-(sum of zeroes) x+product of zeroes =0

Therefore required quadratic equation is

x²-6x+7=0