Question

f(x) is polynomial of degree 'n' with rational coefficients and 1+2i, 2-root3
5 are the three zeroes of f(x). Then the least value of 'n' is
1)5 2)4 3)3 4)6​

Answer 1

Answer:

correct option 1 :-5

Step-by-step explanation:

The coefficients are rational, the roots should be either rational or if irrational or complex, must occur in pairs with their conjugates.

∵1+2i,2−

3

and 5 are the three roots given.

The irrational root 2−

3

will have its conjugate 2+

3

a root as well.

Similarly, 1−2i is also a root.

∴ there exist at least 5 roots of f(x)=0 and hence least value of n is 5.