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ICE Princess25 [194]
3 years ago
6

Knowing that 2i is one answer to the equation x^4 - 2x^3 + 6x^2 - 8x + m = 0, find the 'm' and the other possible answers.

Mathematics
1 answer:
kakasveta [241]3 years ago
4 0
Ok so remember
if a+bi is a root, then a-bi is also a root

since 2i is a root, -2i is also a root
use synthetic division and the fact that when we divide by 2i and -2i, we have to get all real coeficients and end witha zero at the end
I will show the division in the attachment

we find m=8


we then find th resulting equation that is x^2-2x+2=0
quadratic formula
x=\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}
x=1+i or 1-i







m=8 and the other roots are
x=-2i, 1+i, 1-i


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Two corresponding sides of similar triangles are 2 cm and 5 cm. What is the area of the second triangle if the area of the first
Stella [2.4K]

Answer:

(1) Area of second triangle= 50 cm^2.

(2) Area of ΔABC=98 cm^2.

   and Area of ΔDFG=175 cm^2.

Step-by-step explanation:

<em>" For two similar triangles the ratio of sides is equal to the ratio of square of their areas".</em>

i.e. if a,b are the corresponding sides of two similar triangles and let A and B denote the area of two triangles then we have the relation as:

\dfrac{a^2}{b^2}=\dfrac{A}{B}

(1)

for the first question:

we have a=2, b=5.

A=8 cm^2.

Hence,

\dfrac{2^2}{5^2}=\dfrac{8}{B}\\\\\dfrac{4}{25}=\dfrac{8}{B}

B=50 cm^2.

Hence, the area of second triangle is 50 cm^2.

(2)

In second option we have:

a=6 and b=5.

A-B=77 cm^2.

A=77+B

\dfrac{6^2}{5^2}=\dfrac{A}{B}\\  \\\dfrac{36}{25}=\dfrac{77+B}{B}\\  \\36B=25\times77+25B\\\\36B-25B=25\times77\\\\11B=25\times77\\\\B=25\times7\\\\B=175

Hence area of second triangle i.e. ΔDFG is 175 cm^2.

and area of first triangle i.e. ΔABC=175-77=98 cm^2.




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