Question

If the one of the zero of the polynomial is x2 - 4x + 1 is (2 + √3), write the other two zeros..for exams ...so please . give genuine answers...student written. ..​

Answer 1

Answer:

$2 - \sqrt{3}$

See actually we can answer this using symmetrical roots of a quadratic

i.e. they appear in pairs

for eg if one root is $4 - \sqrt{3}$ then the other root will be $4 + \sqrt{3}$

same goes for the imaginary roots

if one root $a + bi$ then the other root is $a - bi$

this can be understood using the quadratic formula as well

Using this symmetry we can even say that quadratic will have either two rational roots or two irrational roots or  two imaginary roots...... there is no such quadratic which has one irrational and one rational roots

Hope this helps