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2 years ago

SHOW that (x + 3) and (x - 2) are factors of f(x) = x4 + 10x3 + 23x2 - 34x - 120.

1 answer:

8 0

If f(x) = 0 then it is a root

x + 3 = 0
x=-3
f(-3) = (-3)^4 + 10(-3)^3 + 23(-3)^2 - 34(-3) - 120 = 0

x - 2 = 0
x=2
f(2) = (2)^4 + 10(2)^3 + 23(2)^2 - 34(2) - 120 = 0

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Step-by-step explanation:

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$2\times \frac{1}{2}\pi r^2\\\\=\frac{22}{7}\times \frac{45}{2}\times \frac{45}{2}\\\\=\frac{445500}{28}\ in^2$

And the combined area of the semicircles is given by

$\frac{4950}{7}+\frac{445500}{28}\\\\=\frac{465300}{28}\ in^2$

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$Length\times width\\\\=AD\times AB\\\\=45\times 30\\\\=1350\ in^2$

Hence, Ratio of the area of the rectangle to the combined area of the semicircles is given by

$1350:\frac{465300}{28}\\\\=1350\times 28:465300\\\\=37800:465300\\\\=84:1034$

Hence, the required ratio will be

$84:1034$

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The ratio of the number of chocolates that contain nuts to the number of chocolates = 1:4

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