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2 years ago

Find the discriminant, describe the types of roots, and find the solution for 3x^2-24x+12

1 answer:

4 0

The discriminant of a polynomial is given by:
b ^ 2-4ac
Substituting the values we have:
(-24) ^ 2-4 * (3) * (12) = 432
Since the discriminator is greater than zero, then the roots are real.
x = (- b +/- root (b ^ 2-4ac)) / (2a)
Substituting the values:
x = (- (- 24) +/- root (432) / (2 * (3))
x = (- (- 24) +/- root (432) / (2 * (3))
x = (- (- 24) +/- root (144 * 3) / (2 * (3))
x = (24 +/- 12raiz (3) / (6)
x = 4 +/- 2raiz (3)
The roots are:
x1 = 4 + 2raiz (3)
x2 = 4 - 2raiz (3)
Answer:
432
the roots are real.
x1 = 4 + 2raiz (3)
x2 = 4 - 2raiz (3)

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the total area is 15.6 square units

Step-by-step explanation:

hello,

you can find the total area dividing the shape into two known shapes

total area= area of the trapezoid +area of the semicircle

then

step one

find the area of the isosceles trapezoid using

$A=\frac{a+b}{2}*h$

where

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let

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put the values into the equation

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Step two

find the area of the semicircle

the area of a circle is given by

$A_{c}=\pi \frac{d^{2}}{4}\\$

but, we need the area of half circle, we need divide this by 2

$A_{semic}=\frac{ \pi \frac{d^{2}}{4}}{2}\\A_{semic}= \pi \frac{d^{2}}{8}$

now the diameter of the semicircle is 2, put this value into the equation

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find the total area

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$total\ area= 14+\frac{\pi }{2} \\total\ area=15.6$

so, the total area is 15.6 square units

Have a good day.

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