Form a polynomial f x with real coefficients having the gi

Form a polynomial f ( x ) with real coefficients having the given degree and zeros. Degree 5, zeros - 9, -i, 3+i

Solution

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Given a polynomial of degree 5 aand zeroes as 9, -i, 3+ i

Now we know that complex roots always occur is pair. Therefore if -i is a zero => +i is also a zero . Similarly 3 - i is also a root of polynomial.

f(x) : (x - 9)(x+ i) (x - i) ( x - 3 - i) (x - 3 + i) = 0

f(x) : (x - 9)(x^2 + 1)( (x - 3)^2 + 1) = 0

f(x) : (x^3 - 9x^2 + x - 9)( x^2 - 6x + 10) = 0

f(x) : (x^5 - 15x^4 + 65x^3 - 105x^2 + 64x - 90) = 0

Solution