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Helga [31]
3 years ago
7

The solution to 3x2 – 12x 24 = 0 is

Mathematics
2 answers:
Marrrta [24]3 years ago
8 0

The answer will be B. 2+2i or 2-2i.

zzz [600]3 years ago
7 0
3x^2 - 12x + 24 = 0 \\ x^2 - 4x + 8 = 0 \\ x= \frac{-b \pm  \sqrt{ b^{2} -4ac} }{2a} 
; where a = 1, b = -4 and c = 8
x= \frac{-(-4) \pm \sqrt{ (-4)^{2} -4 \times 1 \times 8} }{2 \times 1} \\ = \frac{4 \pm \sqrt{ 16 -32} }{2} \\ =\frac{4 \pm \sqrt{ -16} }{2} \\ =\frac{4 \pm 4i }{2} \\ =2+2i \ or \ 2-2i
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Determine whether the set of vectors is a basis for ℛ3. Given the set of vectors , decide which of the following statements is t
schepotkina [342]

Answer:

(A) Set A is linearly independent and spans R^3. Set is a basis for R^3.

Step-by-Step Explanation

<u>Definition (Linear Independence)</u>

A set of vectors is said to be linearly independent if at least one of the vectors can be written as a linear combination of the others. The identity matrix is linearly independent.

<u>Definition (Span of a Set of Vectors)</u>

The Span of a set of vectors is the set of all linear combinations of the vectors.

<u>Definition (A Basis of a Subspace).</u>

A subset B of a vector space V is called a basis if: (1)B is linearly independent, and; (2) B is a spanning set of V.

Given the set of vectors  A= \left(\begin{array}{[c][c][c][c]}1 & 0 & 0 & 0\\ 0 & 1 & 0 & 1\\ 0 & 0 & 1 & 1\end{array} \right) , we are to decide which of the given statements is true:

In Matrix A= \left(\begin{array}{[c][c][c][c]}(1) & 0 & 0 & 0\\ 0 & (1) & 0 & 1\\ 0 & 0 & (1) & 1\end{array} \right) , the circled numbers are the pivots. There are 3 pivots in this case. By the theorem that The Row Rank=Column Rank of a Matrix, the column rank of A is 3. Thus there are 3 linearly independent columns of A and one linearly dependent column. R^3 has a dimension of 3, thus any 3 linearly independent vectors will span it. We conclude thus that the columns of A spans R^3.

Therefore Set A is linearly independent and spans R^3. Thus it is basis for R^3.

8 0
3 years ago
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asambeis [7]

Answer:

Step-by-step explanation:

An equation contains a sign equality (=) between two expressions.

And an expression is a simple algebraic statement.

By these definitions,

          Equations                          Expressions

         x = 2x + 5                            21x - 13 + 11x

         \frac{1}{2}x=5+3                           -3.7x - 13  

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7 0
3 years ago
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