Question

if one root of a quadratic equation with rational coefficient is 2+√3 then the other root is

Answer 1

One root is = (-4)+(7)^1/2 ,

Another root will be (-4)-(7)^1/2

Sum of roots =(-4)+(7)^1/2+(-4)-(7)^1/2= -8

Product of roots =(-4)^2-(7^1/2)^2

=16–7

=9

Eq. is:-

x^2-(-8).x+9=0

x^2+8 x+9=0 , Answer.

Answer 2

2 - $\sqrt{3}$

Step-by-step explanation:

Given that,

One root of a quadratic equation having a rational coefficient = $2 + \sqrt{3}$

To find,

The other root = ?

Procedure:

As we know,

A quadratic equation having a rational coefficient has conjugate roots.

Thus,

The other root will be 2 - $\sqrt{3}$

Learn more: quadratic equation

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