Question

find a quadratic polynominals whose zeroes are 5-3√2 and 5+3√2​

Answer 1

Step-by-step explanation:

Here, Let the two zeros are

α = 5-3√2 and. β = 5+3√2....

then, general equation of quadratic formula is

$f(x) = {x}^{2} - ( \alpha + \beta )x + \alpha \beta$

so,

$\alpha + \beta$

$= 5 - 3 \sqrt{2} + 5 + 3 \sqrt{2}$

$= 10$

and,

$\alpha \beta$

$= (5 - 3 \sqrt{2} )(5 + 3 \sqrt{2} )$

$= 25 - 18$

$= 7$

then, the quadratic equation are...

$f(x) = {x}^{2} - ( \alpha + \beta )x + \alpha \beta$

$or \: \: f(x) = {x}^{2} - 10x + 7 = 0$

thanks a lot...