Apolynomial equation with rational coefficients has the roots 3+ square root 6, 2- square root 5. find the two additional roots

Step-by-step explanation:

If a polynomial equation with rational coefficients is , then by quadratic formula

where, a,b and c are rational number.

If is an irrational number, then we have ± sign before the irrational number.

It is given that are two roots of a polynomial equation with rational coefficients. Here, are irrational numbers.

So, the root of the polynomial equation are

Therefore, the remaining roots of the polynomial equation are .

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.