How do you find all the zeros of P(x)=x^4+6x^2+9P(x)=x4+6x2+9?
1 Answer
Mar 4, 2016
Explanation:
The polynomial is of a biquadratic kind so, making
And equating the polynomial to zero we have
Delta=-36-36=0
y=(-6+-0)/2 =>y_1=y_2=-3
Then
x_(1,2)=sqrt(y_1)=sqrt(-3) =>x_1=i*sqrt(3) ,x_2=-i*sqrt(3)
x_(3,4)=sqrt(y_2)=sqrt(-3) =>x_3=i*sqrt(3) ,x_4=-i*sqrt(3)
So
x_1=x_3=i*sqrt(3)
x_2=x_4=-i*sqrt(3)