Question

from a quadratic polynomial whose zeroes are 2+√3 and 2-√3​

Answer 1

Step-by-step explanation:

Zeroes are 2 + √3 and 2 - √3

Factors will be ( x - 2 - √3 ) and ( x - 2 + √3 )

When we multiply these factors, we will get the polynomial.

(x -2 - √3)(x - 2 + √3)

= x² - 2x + √3x - 2x + 4 -2√3 - √3x + 2√3 - 3

= x² + x ( -2 + √3 - 2 - √3 ) + 4 - 3

Hence the polynomial is

x² - 4x + 1

Answer 2

zeroes are 2+√3 and 2-√3

sum of roots = a+b = (2+√3 )+( 2-√3)= 4

product of roots = a×b = (2+√3) × ( 2-√3) = 2²-√3² = 4-3 = 1

standard form x²-(a+b) +ab =0

x² -4x +1 = 0