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PSYCHO15rus [73]
3 years ago
12

Using the Factor Theorem, which of the polynomial functions has the zeros 4,

Formula1" title="\sqrt7" alt="\sqrt7" align="absmiddle" class="latex-formula">, and -\sqrt{7\\}?
f (x) = x3 – 4x2 + 7x + 28
f (x) = x3 – 4x2 – 7x + 28
f (x) = x3 + 4x2 – 7x + 28
f (x) = x3 + 4x2 – 7x – 28
Mathematics
1 answer:
Serjik [45]3 years ago
8 0

Answer:

B

Step-by-step explanation:

According to the Factor Theorem, if (<em>x</em> - <em>a</em>) is a factor (where <em>a</em> is a zero) of the polynomial P(x), then P(a) must equal zero.

Our zeros are 4, √7, and - √7. Hence, when evaluating P(4), P(√7), and P(-√7), all must evaluate to zero.

Testing each choice, we can see that only choice B is true. That is:

\displaystyle \displaystyle \begin{aligned} f(4)&= (4)^3 - 4(4)^2 - 7(4) + 28 \\ &= (64) - (64) - (28) + 28 \\ &= 0 \stackrel{\checkmark}{=}0 \\f(\sqrt{7}) &= (\sqrt{7})^3 - 4(\sqrt{7})^2 - 7(\sqrt{7}) + 28 \\ &= (7\sqrt{7}) - (28) - (7\sqrt{7}) + 28 \\ &= 0 \stackrel{\checkmark}{=} 0\\ f(-\sqrt{7}) &= (-\sqrt{7})^3 - 4(-\sqrt{7})^2 - 7(-\sqrt{7}) + 28 \\ &= (-7\sqrt{7}) - (28) + (7\sqrt{7}) + 28 \\ &= 0 \stackrel{\checkmark}{=} 0  \end{aligned}

In conclusion, our answer is B.

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