Question
State the possible number of imaginary zeros of g(x)= x4 + 3x3 + 7x2 - 6x - 13.
I came up with the answer of 2,4 or 0.
Is this correct?
Thanks for your help.
I came up with the answer of 2,4 or 0.
Is this correct?
Thanks for your help.
Answers
Substitute x = i t where t is assumed to be real:
t^4 - 3it^3 - 7t^2 -6 i t - 13 = 0
Take the imaginary part of the equation:
t^3 + 2 t = 0 --->
t(t^2 + 2) = 0
Now, we can see from the original equation for t that t = 0 is not a solution (this is actually implied by the real part of the equation). Since t has to be real, the equation:
t^2 + 2 = 0
cannot be satisfied.
Therefore the equation has no imaginary solutions.
t^4 - 3it^3 - 7t^2 -6 i t - 13 = 0
Take the imaginary part of the equation:
t^3 + 2 t = 0 --->
t(t^2 + 2) = 0
Now, we can see from the original equation for t that t = 0 is not a solution (this is actually implied by the real part of the equation). Since t has to be real, the equation:
t^2 + 2 = 0
cannot be satisfied.
Therefore the equation has no imaginary solutions.
Related Questions
State the possible number of imaginary zeros of g(x)= x^4+3x^3+7x^2-6x-13
this is how far Ive gott...
Do you have any ny state number and operation booklets for 7th graders.
State the possible number of imaginary zeros of f(x)= 2x^3 - 4x^2 + 8x - 3.
0,1,3?
12. State whether the number 97 is prime, composite, or neither.
In a certain state, the number of individuals age 65 or older has steadily increased with each passi...
State the number of electrons lost or gained when the following elements form ions.
Group 3A (3)
for each zero state number of its multiplicity
x=-5
x=3/2
State the maximum number of turns the graph of each function could make. F(x)=-x^3+2x^2
state whether the number is a solution tot he given number inequality
X equal to less than - 17;...
State the possible number of positive real zeroes, negative real zeroes, and imaginary zeroes of eac...