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2 years ago

What are the roots of the equation 16x2 + 40x + 27 = 0 in simplest a + bi form?

Mathematics

1 answer:

bezimeni [28]2 years ago

7 0

9514 1404 393

Answer:

-5/4 +i(√2)/4 and -5/4 -i(√2)/4

Step-by-step explanation:

I find simplest form to be easier to get to if the leading coefficient is 1. Dividing by 16, we have ...

x^2 +5/2x +27/16 = 0

Completing the square by adding and subtracting the square of half the x-coefficient, we get ...

(x^2 +5/2x +25/16) +27/16 -25/16 = 0

(x +5/4)^2 = 2/16

Subtracting 2/16, taking the square root, and subtracting 5/4 gives ...

x +5/4 = ±√(-2/16)

x = -5/4 ±i(√2)/4

The roots are -5/4 +i(√2)/4 and -5/4 -i(√2)/4.

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Complete the squar3

cricket20 [7]

9514 1404 393

Answer:

4
-2
4
2
-2±√2

Step-by-step explanation:

In order to fill the first blank, we need to look at the second line to see what the coefficient of x is.

1. x² + 4 x +2 = 0

The constant is subtracted from both sides to get the second line.

2. x² +4x =  -2 

The value that is added on the third line is the square of half the x-coefficient: (4/2)² = 4

3. x² +4x + 4  = -2 +4

On the fourth line, the left side is written as a square, and the right side is simplified. The square root is taken of both sides.

4. √(x +2)² = ±√ 2 

Finally, 2 is subtracted from both sides to find the values of x.

5. x =  -2 ±√2 

8 0

1 year ago

Which model represents the product 3/4 x 1/3

dlinn [17]

Answer:

The first one

Step-by-step explanation:

5 0

1 year ago

There are five identical blue books, two identical green books, and three identical black books. How many different patterns can

dsp73

Answer:

2520 patterns

Step-by-step explanation:

In 'n' 10! ways, books can be arranged. But, there are also 5! permutation of blue books 'n1', 2! permutation of identical green books 'n2', and 3! permutation identical black books 'n3'.

Therefore, for non identical arrangements:

$\frac{n!}{n1!n2!n3!}$

$\frac{10!}{5!2!3!}$ = 2520

Therefore, the books can be arranged on a shelf in 2520 patterns

8 0

2 years ago

A textbook store sold a combined total of 260 chemistry and physics textbooks in a week. The number of chemistry books sold was

Lynna [10]

Let:

x = Chemistry textbooks sold

y = Physics textbooks sold

The textbook store sold a combined total of 260, so:

$x+y=260$

The number of chemistry books sold was three times the number of physics textbooks sold, so:

$x=3y$

Let:

$\begin{gathered} x+y=260_{\text{ }}(1) \\ x=3y_{\text{ }}(2) \end{gathered}$

Replace (2) into (1):

$\begin{gathered} 3y+y=260 \\ 4y=260 \\ y=\frac{260}{4} \\ y=65 \end{gathered}$

Replace the value of y into (2):

$\begin{gathered} x=3(65) \\ x=195 \end{gathered}$

5 0

5 months ago

What is the minimum force required to prevent a ball weighing 22.6 lb from rolling down a ramp which is inclined at 39.0 with th

shusha [124]

22.6sin[39.0]= 21.78

3 0

2 years ago