form a polynomial f(x) with real coefficients having the given degree and zeros degree 5; zeros 7; -i; -8+i enter the polynomial f(x)a=?

Question

campbell_st · Answer

well you need the conjugate pairs for the complex roots

f(x) = a(x -7)(x -i)(x + i)(x -(8+i))(x +(8+i))

hope it helps

anonymous · Answer

yes that helped then what is next

campbell_st · Answer

well why not distribute... 

(x -i)(x + i) = x^2 = -1

or x^2 + 1

anonymous · Answer

ok

campbell_st · Answer

so you have 

f(x) = a(x -7)(x^2 + 1)(x -(8+i))(x +(8 + i))

just keep distributing...

anonymous · Answer

yes i did that but now im stuck

campbell_st · Answer

ok... so the other quadratic factor is 

$$(x -(8 + 1))(x +(x +i)) = x^2 - (8 + i)^2$$

anonymous · Answer

ok so what will  f(x)a=

campbell_st · Answer

well it should be 

f(x) =a(.......)

becuase f(x) may be a multiply of the equation 

e.g.

roots x = 2, 3

f(x) = a(x -2)(x -3)

f(x) = a(x^2 -5x + 6)

the value of a is found by substituting a point thats on the curve and then solving for a.

anonymous · Answer

ok thank you