Question

find the quadratic polynomial
whose zeroeses are 2+√3 and 2-√3​

Answer 1

Solution

Given :-

• Zeroes of any polynomial , ( 2 + √3) & ( 2 - √3)

Find :-

• Equation of polynomial

Explanation,

Let,

• Zeroes of polynomial, p & q

So,

==> Sum of zeroes = ( 2 + √3)+(2-√3)

==> p + q = 4 -----------(1)

And,

==> product of zeroes = ( 2 + √3) * (2-√3)

==> p . q = ( 2² - √3²)

==> p . q = ( 4 - 3)

==> p . q = 1 ------------(2)

Formula Of Equation,

[ x² - ( Sum of zeroes ) x + ( product of zeroes ) = 0 ]

Keep Value by equ(1) & equ(2)

==> x² - 4x + 1 = 0

Hence

• Required Equation, x² - 4x + 1 = 0

_________________