# Algebra II

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?

1. 👍 0
2. 👎 0
3. 👁 87
1. 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.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Algebra II

State the number of positive real zeros, negative real zeros, and imaginary zeros for g(x)= 9x3 -7x2+10x-4. Since there were 3 sign changes I have 3 positive real zeros. For g(-x)= I have -9x3-7x2-10x-4. There were no sign changes

asked by Lucy on February 17, 2008
2. ### Algebra

State the possible number of imaginary zeros of g(x)= x^4+3x^3+7x^2-6x-13 this is how far Ive gotten:there are 4 zeros,3 positive and 1 negative If you've found four real zeroes, then there are no imaginary zeroes. You can also

asked by Marissa on August 10, 2007
3. ### Math

State the number of positive real zeros, negative real zeros, and imaginary zeros for g(x)= 9x^3 - 7x^2 + 10x - 4. The only thing I know is that there are 3 sign changes.

asked by Jon on March 3, 2008
4. ### algebra2

state the number of positive real zeros, negative real zeros, and imaginary zeros for g(x) = 9x^3 - 7x^2 +10x - 4

asked by aisha on December 22, 2009
5. ### Algebra 2

State the possible number of imaginary zeros of f(x)= 2x^3 - 4x^2 + 8x - 3. 0,1,3?

asked by Lily on May 18, 2013
6. ### algebra

1)Use synthetic subsitution to find f(-3)for f(x)=x^4-4x^3+2x^2-4x+6 answer= -15 2)One factor of x^3+2x^2-11x-12 is x+4. find the remaining factors answer= x-1;x-3 3)Which describes the number and type of roots of the equation

asked by Marissa on August 17, 2007
7. ### Maths

x2-x-6 is a factor of f(x)=3x3+px2+qx+6. Find the values of the constants p and q and state the zeros of f(x).

asked by Ande2 on November 21, 2018
8. ### math

approximate all zeros and extrema to the nearest hundredth. how many zeros, if any, are imaginary. -x^4+2x^2+x-4. Are there no zeros?

asked by anonymous on October 1, 2016
9. ### Math

Which of the following are linear equations in x1, x2 and x3? (a) x1 + 5x2 − (2^0.5)x3 =1 (b) x1 + 3x2 + x1.x3 = 2 (c) x1 = −7x2 + 3x3 (d) x1^−2 + x2 + 8x3 =5 (e) x1^3/5 − 2x2 + x3 = 4 (f) πx1 − (2^0.5)x2 + 13x3 = 7^1/3

asked by Matt on October 25, 2011
10. ### algebra

1)A.f(x)= x^2+4 B.f(x)= x^2-4x^2+4x-16 C.f(x)= x^2+4x^2+4x+16 D.f(x)= x^2-4x^2-4x+16 2)A.+-1,+-2,+-3,+-6 B.0,+-1,+-2,+-3,+-6,+-1/3,+-2/3 C.+-1,+-2,+-3,+-6,+-1/3,+-2/3 D.+-1,+-3,+-1/6,+-1/3,+-1/2,+-3/2 4)I don't know what they mean

asked by Marissa on August 17, 2007

More Similar Questions