All categories

3 years ago

A^2-a+12=0 I need the roots

Mathematics

1 answer:

kumpel [21]3 years ago

8 0

Answer:

a = 1/2 (1 ±sqrt(47))

Step-by-step explanation:

a^2-a+12=0

We will complete the square

Subtract 12 from each side

a^2-a+12-12=0-12

a^2-a=-12

The coefficient of a = -1

-Divide by 2 and then square it

(-1/2) ^2 = 1/4

Add it to each side

a^2 -a +1/4=-12 +1/4

(a-1/2)^2 = -11 3/4

(a-1/2)^2= -47/4

Take the square root of each side

sqrt((a-1/2)^2) =sqrt(-47/4)

a-1/2 = ±i sqrt(1/4) sqrt(47)

a-1/2= ±i/2 sqrt(47)

Add 1/2 to each side

a-1/2+1/2 = 1/2± i/2 sqrt(47)

a = 1/2± i/2 sqrt(47)

a = 1/2 (1 ±sqrt(47))

You might be interested in

12 10,9,68,12<br> What is the most appropriate measure of center?

valentina_108 [34]

Answer: The most appropriate measure of center is the median.

Step-by-step explanation:

The measure of center generally represented by 1) mean 2) median 3) mode.
Mean is the best measure to represent the center of the data but when data have outliers it gets affected badly.
In that case, we use the Median as the best measure of center.

The given data is 12 10,9,68,12 .

As it can be seen that, the data have extreme value 68 ( called outliers).

In this case, we will use the Median as the best measure of center.

So, the most appropriate measure of center is the median.

5 0

3 years ago

Help w this pls!!!! 20 points

cluponka [151]

You forgot to attach the question…

5 0

3 years ago

Use the distributive property to simplify this expression -2x(3x + x-5)

kvasek [131]

Answer:

− 8 x ^2 + 10 x

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Laila bought 20 strawberries . She ate 1 strawberry what percentage of strawberries did Laila eat?

laiz [17]

5% of the strawberries.

4 0

3 years ago

Read 2 more answers

Chose parameters h and k such that the system has a) a unique solution, b) many solutions, and c) no solution. 31+3x2= 4 2x1+kx2

Snezhnost [94]

Answer

a) k=7, h=9, the unique solution of the system is $(x_1,x_2)=(1,1)$

b) If k=6 and h=8 the system has infinite solutions.

c)If k=6 and h=9 the system has no solutions.

Step-by-step explanation:

I am assuming that the system is x1+3x2=4; 2x1+kx2=h

The augmented matrix of the system is $\left[\begin{array}{ccc}1&3&4\\2&k&h\end{array}\right]$ . If two times the row 1 is subtracted to row 2 we get the following matrix $\left[\begin{array}{ccc}1&3&4\\0&k-6&h-8\end{array}\right]$ .

Then

a) If k=7 and h=9, the unique solution of the system is $x_2=\frac{9-8}{7-6}=\frac{1}{1}=1$ and solviong for $x_1$ ,

$x_1+3x_2=4\\\\x_1=4-3(1)=1$

Then the solution is $(x_1,x_2)=(1,1)$

b) If k=6 and h=8 the system has infinite solutions because the echelon form of the matrix has a free variable.

c)If k=6 and h=9 the system has no solutions because the last equation of the system of the echelon form of the matrix is $0x_2=1$

8 0

4 years ago