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Makovka662 [10]
3 years ago
12

Solve the equation 12a3 + 12a2 = -3a. Show all work.

Mathematics
1 answer:
Artist 52 [7]3 years ago
7 0

12a³ + 12a² = -3a       | + 3a

12a³ + 12a² + 3a = 0

3a(4a² + 4a + 1) = 0

3a(2a + 1)² = 0

3a = 0 or (2a + 1)² = 0

1) 3a = 0      | : 3

a = 0

2) (2a + 1)² = 0

2a + 1 = 0           | - 1

2a = -1           | : 2

a = -1/2

a ∈ {-1/2, 0}

Used formula:

(a + b)² = a² + 2ab + b²

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Answer:

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Step-by-step explanation:

Consider the provided information.

A: When multiplying or dividing rational numbers, when will the answer be positive?

If we are multiplying or dividing rational numbers the answer will be positive if and only if both the rational numbers have same sign.

For example: Multiply 2 and 4.

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or

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B: When multiplying or dividing rational numbers, when will the answer be negative?

If we are multiplying or dividing rational numbers the answer will be negative if and only if both the rational numbers have different sign.

For example: Multiply 2 and -4.

2×-4=-8              (different sign)

or

Multiply -2 and 4.

-2×4=-8             (different sign)

-8 is a negative rational number.

Now divided 2 and -4.

\frac{2}{-4} =-\frac{1}{2}

or

Divided -2 and 4.

\frac{-2}{4} =-\frac{1}{2}

-1/2 is a negative rational number

Hence,  If the signs of rational numbers are different, then the answer is negative.

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