A polynomial equation with rational coefficients has the roots 3+ square root 6, 2- square root 5. Find the two additional roots

Question

asked Sep 20, 2018 69.8k views

2 Answers

Bethel · Answer 1 · 2018-09-25T23:41:01+0000

Answer:

(3-√(6)) and (2+√(5))

Explanation:

If a polynomial equation with rational coefficients is
ax^2+bx+c=0 , then by quadratic formula

$x=(b\pm√(b^2-4ac))/(2a)$

where, a,b and c are rational number.

If
√(b^2-4ac) is an irrational number, then we have ± sign before the irrational number.

It is given that
(3+√(6)) and (2-√(5)) are two roots of a polynomial equation with rational coefficients. Here,
√(6) and √(5) are irrational numbers.

So, the root of the polynomial equation are

$(3\pm √(6)) and (2\pm √(5))$

Therefore, the remaining roots of the polynomial equation are
(3-√(6)) and (2+√(5)) .