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Svetradugi [14.3K]
3 years ago
5

I need help with number 12 please

Mathematics
2 answers:
harina [27]3 years ago
7 0
Yeah your right :) :) :) :)

Contact [7]3 years ago
3 0
The answers that you put are right.
Good job!
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Find the roots of:
Elena-2011 [213]

\large\displaystyle\text{$\begin{gathered}\sf \pmb{1) \  2x^3-7x^2+8x-3=0 } \end{gathered}$}

Synthetic division is used since the equation is of the third degree. The divisors of -3 are 1, -1, 3, +3. So:

  | 2  -7    8  -3

<u>1 |      2   -5   3</u>

  | 2   -5    3  0

<u> 1 |      2     -3   </u>

    2   -3     0

So the factorization is (x-1)² (2x-3)=0. So:

                     \bf{ x_1=x_2=1 \qquad x_2=\dfrac{3}{2}  }

\large\displaystyle\text{$\begin{gathered}\sf \pmb{2) \  x^3-x^2-4=0 } \end{gathered}$}

Synthetic division is used since the equation is of the third degree. The divisors of -4 are 1, -1, 2, -2, 4, -4. So:

      |  1  -1  0  -4

  <u>2  |     2  2     </u>

         1  2  2  0

So the factorization is (x-2)(x²+x+2)=0 . When calculating the discriminant of the trinomial, it is concluded that it has no roots since the result is negative. So you only have one solution.

                   \bf{ 1^2-4(2)(2)=1-16=-15 < 0 \quad \Longrightarrow \quad x=2 }

\large\displaystyle\text{$\begin{gathered}\sf \pmb{3) \  6x^3+7x^2-9x+2=0 } \end{gathered}$}

Synthetic division is used since the equation is of the third degree. The divisors of 2 are 1, -1, 2, -2. So:

   | 6    7       9      2

<u>-2 |      -12    10     -2</u>

     6    -5     1       0

So the factorization is (x+2)(6x²-5x+1)=0 . The quadratic equation is solved by the general formula:

         \bf{ x_{2, 3}&=\dfrac{5\pm \sqrt{(5)^2-4(6)(1)}}{2(6)}=\dfrac{5\pm \sqrt{25-24}}{12}=\dfrac{5\pm 1}{12} }}

                     \large\displaystyle\text{$\begin{gathered}\sf  \begin{matrix} x_1=-2&\ \ \ \ \ \ x_{2}=\dfrac{6}{12} \qquad &\ \ \ x_3=\dfrac{4}{12}\\ &\ \ \ x_2=\dfrac{1}{2} \qquad &x_3=\dfrac{1}{3} \end{matrix} \end{gathered}$}

6 0
2 years ago
Systems of equations with different slopes and different y-intercepts have more than one solution.
FrozenT [24]

Answer: OPTION C.

Step-by-step explanation:

The systems of linear equations can have:

1. <u>No solution:</u> When the lines have the same slope but different y-intercept. This means that the lines are parallel and never intersect, therefore, the system of equations has no solution.

2. <u>One solution</u>: When the lines have different slopes and intersect at one point in the plane. The point of intersection will be the solution of the system

3. I<u>nfinitely many solutions</u>: When the lines have the same slope and the y-intercepts are equal. This means that the equations represents the same line and there are infinite number of solution.

Therefore, based on the explained above, the conclusion is: Systems of equations with different slopes and different y-intercepts <em><u>never</u></em> have more than one solution.

7 0
3 years ago
Which property is illustrated by 45+19=19+45
MariettaO [177]
The property that is illustrated is the Commutative Property Of Addition. This is because there are no parenthesis, the numbers switch order, and the answer remains the same.
6 0
3 years ago
Help me with this problem I've been working on it for a while now and just can't figure it out
MA_775_DIABLO [31]
It simplifies down to x + 4
 Hope I helped C:
5 0
3 years ago
6.
PilotLPTM [1.2K]

Answer:

y=-2x-4

Step-by-step explanation:

The slope has a Y-intercept at the -4, which narrows the choices down to 2. Since the slope is leaning left, it's a negative, which will make the answer to this y=-2x-4

7 0
3 years ago
Read 2 more answers
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