Question

find the quadratic polynomial of zeroes (√2+√3).(√2-√3)​

Answer 1

Answer:

Step-by-step explanation:

quadratic equation = x^2 - (a+b)x + ab

= x^2 - (2root2)x + 4

Answer 2

Question :-

Find the quadratic polynomial of zeros (√2+√3) ,

(√2 - √3) .

Answer :-

→ x² - 2√2x -1 = 0

Solution :-

We have zeros → (√2+√3) and (√2 - √3) .

We know that ,

if we have zeros a and b ,then quadratic polynomial is -

→ x² - ( sum of zeros )x + product of zeros = 0 .

So ,firstly we will have to find sum of roots and

product of roots .

therefore ,

$\to \sf Sum \: of \: zeros = ( \sqrt{2} + \sqrt{3} )</p><p> + ( \sqrt{2} - \sqrt{3} ) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \sqrt{2} \\ \\ \to \sf product \: of \: roots \: = ( \sqrt{2} + \sqrt{3} )( \sqrt{2} - \sqrt{3)} \\ \\ \boxed{ \because \sf(a + b)(a - b) = {a}^{2} - {b}^{2} } \: \\ \\ \to \sf product \: of \: zeros\: = {( \sqrt{2}) }^{2} - {( \sqrt{3} )}^{2} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 - 3 = - 1$

hence quadratic polynomial is -

→ x² - (sum of zeros )x + product of zeros = 0

→ x² - 2√2x -1 = 0