Question

find the quadratic polynomial the sum and product of whose zeros are 2 + √3 and 2 - √3 respectively​

Answer 1

Answer:

let A and B be the sum and product of roots

then,

A = 2 + √3 and

B = 2 -√3

so,

required quadratic equations is

x² - (A + B)x + AB = 0

Or

x² -( 2 + √3)x + 2 - √3 = 0

Answer 2

Question :-

→ Find the quadratic polynomial ,whose sum of zeros and product of Zeros are 2+√3 and 2-√3 respectively .

Answer :-

$\to \boxed{\sf{{x}^{2} - (2+\sqrt{3})x +2-\sqrt{3} = 0}}$

To Find :-

→ Quadratic polynomial .

Explanation :-

According to the question

→ 2+√3 and 2 -√3 are the sum of zeros and product of zeros respectively.

We know that

We know that ( if we have zeros) then its quadratic equation is -

→ X² - (sum of zeros )x + Product of zeros = 0

→ X² - (2 + √3)x + 2-√3 = 0

This is the required quadratic polynomial.

Verification of zeros :-

We know that -

$\boxed{ \sf{product \: of \: zeros = \frac{constant}{coefficient \: of \: {x}^{2}}}} \\ \\ \implies \: \frac{2-\sqrt{3}}{1} = 2-\sqrt{3}\\ \\ \boxed{ \sf{sum \: of \: zeros = \frac{ - coefficient \: of \: x}{coefficient \: of \: {x}^{2}}}} \\ \\ \implies \: \frac{2+\sqrt{3}}{1} = 2+\sqrt{3}$

hence verified .