Information is given about a polynomial fx whose coefficient

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. Degree 4; zeros: i, 13 + i Enter the remaining zeros of f.

Solution

for a polynoimial with real coefficients ,if complex numbers are the roots then their conjugates are also the roots

given i , 13+i are the roots , so their conjugates -i , 13-i are also the roots

plynomial of degree 4 is

f(x)=(x-i)(x-(13+i))(x-(-i))(x-(13-i))

f(x)=(x-i)(x-(13+i))(x+i)(x-(13-i))

f(x)=(x-i) (x+i)(x-(13+i))(x-(13-i))

f(x)=(x²-(i²))(x²-x(13-i) -(13+i)x +(13+i)(13-i))

f(x)=(x²-(-1))(x²-13x +ix -13x-ix +(13²-i²))

f(x)=(x²+1)(x²-26x +170)

f(x)=x²(x²-26x +170) +(x²-26x +170)

f(x)=(x⁴-26x³ +170x²) +(x²-26x +170)

f(x)=x⁴-26x³ +171x²-26x +170