Find a cubic polynomial function f with real coefficients that has the given complex zeros and x-intercept. Complex Zeroes. x=2\pm\sqrt{2}i

permaneceerc

permaneceerc

Answered question

2021-09-16

Find a cubic polynomial function f with real coefficients that has the given complex zeros and x-intercept. 
Complex Zeroes 
x=2±2i 
X-Intercept (5,0)

Answer & Explanation

tabuordg

tabuordg

Skilled2021-09-17Added 99 answers

The cubic polynomial's zeros are provided.
There are two complex zeros and one real.
complex zeros are 2+2i,22i 
real zeros is 5. 
then factors of the polynomial will be 
x5,x(2+2i),x(22i) 
equation will be 
(x5){x(2+2i)}{x(22i)}=0 
(x5)(x2x(22i)x(2+2i)+(2+2i)(22i))=0 
(x5)(x2x(2+2i+22i)+22(2i)2)=0 
(x5)(x24x+4+2)=0 
(x5)(x24x+4+2)=0 
x34x2+6x5x2+20x30=0 
x39x2+26x30=0 
polynomial will be 
y=a(x39x2+26x30). a0 
there are infinite number of polynomials.

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