In quadratic equations of real coefficients, the complex roots always occur in conjugate bases. It means, if, 2 + 3i is one of the roots and then the second root must be 2 - 3i.

7 0

2 years ago

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What is the area of a triangle with vertices (1,0) (5,0) (3,4)

Aleksandr-060686 [28]

Answer:

The area of the triangle is of 8 units of area.

Step-by-step explanation:

Answer:

The area of the triangle is of 21 units of area.

Step-by-step explanation:

The area of a triangle with three vertices $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ is given by the determinant of the following matrix:

$A = \pm 0.5 \left|\begin{array}{ccc}x_1&y_1&1\\x_2&y_2&1\\1_3&y_3&1\end{array}\right|$

In this question:

Vertices (1,0) (5,0) (3,4). So

$A = \pm 0.5 \left|\begin{array}{ccc}1&0&1\\5&0&1\\3&4&1\end{array}\right|$

$A = \pm 0.5(1*0*1+0*1*3+1*5*4-1*0*3-0*5*1-1*1*4)$

$A = \pm 0.5*(20-4)$

$A = \pm 0.5*16 = 8$

The area of the triangle is of 8 units of area.

3 0

3 years ago

What are the roots of the polynomial equation? x² + 7x + 12 = 0 Enter your answers in the boxes. x1= x2=

oksian1 [2.3K]

The equation factors as
.. (x +3)(x +4) = 0
By the zero-product rule, the roots are
.. x1 = -4
.. x2 = -3

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3 years ago

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let m be the number of months. write an expression to show the total amount deposited after m months.​

let m be the number of months. write an expression to show the total amount deposited after m months.