Question

Determine if the statement is true or false. If a statement is false, explain why. Given $f(x) = 2ix^4 - (4 + 7i)x^3 + 9x^2 + 2$, if $a + bi$ is a zero of $f(x)$, then $a - bi$ must also be a zero. True False The conjugate zeros theorem stipulates that the coefficients of the polynomial must be real. $f(x) = 2ix^4 - (4 + 7i)x^3 + 9x^2 + 2$ does not have real coefficients. $f(x) = 2ix^4 - (4 + 7i)x^3 + 9x^2 + 2$ does have real coefficients.

          Determine if the statement is true or false. If a statement is false, explain why.
Given $f(x) = 2ix^4 - (4 + 7i)x^3 + 9x^2 + 2$, if $a + bi$ is a zero of $f(x)$, then $a - bi$ must also be a zero.
True
False
The conjugate zeros theorem stipulates that the coefficients of the polynomial must
be real.
$f(x) = 2ix^4 - (4 + 7i)x^3 + 9x^2 + 2$ does not have real coefficients.
$f(x) = 2ix^4 - (4 + 7i)x^3 + 9x^2 + 2$ does have real coefficients.

Determine if the statement is true or false. If a statement is false, explain why.
Given f(x) = 2ix^4 - (4 + 7i)x^3 + 9x^2 + 2, if a + bi is a zero of f(x), then a - bi must also be a zero.
True
False
The conjugate zeros theorem stipulates that the coefficients of the polynomial must
be real.
f(x) = 2ix^4 - (4 + 7i)x^3 + 9x^2 + 2 does not have real coefficients.
f(x) = 2ix^4 - (4 + 7i)x^3 + 9x^2 + 2 does have real coefficients.

Added by Michelle G.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Rebecca Belvin

Step 1

To do this, we can substitute a+bi into f(x) and see if it equals zero. f(a+bi) = 2i(a+bi) - (4+7i(a+bi)+9+2) Simplifying this expression, we get: f(a+bi) = 2ia + 2ibi - 4 - 7ia - 7ibi - 9 - 2 Combining like terms, we get: f(a+bi) = (2ia - 7ia) + (2ibi - Show more…

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Determine if the statement is true or false. If a statement is false, explain why. Given f=2ix-(4+7ix+9+2), if a+bi is a zero of f(x), then a-bi must also be a zero. True or False: The conjugate zeros theorem stipulates that the coefficients of the polynomial must be real. f(x)=2ix-(4+71x+9x+2) does not have real coefficients. However, f(x)=2ix-4+7ix+9x+2 does have real coefficients.