Find a polynomial function of lowest degree with rational co

Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. 4+1,3

I hope the zeros are 4+i and 3.

Note: If \'a\' is a zero, the the corresponding zero ix \'x-a\'.

We know that irrational roots always occur in pairs.

So, 4-i is also a zero since 4+i is a zero.

Also 3 is a zero.

So the polynomial is,

P(x) =(x-(4+i)) (x-(4-i)) (x-3)

= (x-4-i)(x-4+i) (x-3)

= ((x-4)²-i²) (x - 3 )

= (x²+16-8x+1)(x-3) (Because i² = -1)

= (x²-8x+17) (x-3)

= x³-8x²+17x -3x²+24x-51

= x³-11x²+41x -51, which is the required polynomial.