How many solutions the equation ( x &#x2212;<!-- − --> 2 ) ( x + 1 ) ( x

Eliaszowyr1

Eliaszowyr1

Answered question

2022-05-22

How many solutions the equation ( x 2 ) ( x + 1 ) ( x + 6 ) ( x + 9 ) + 108 = 0 has in the interval ( 10 , 1 ) ?

Answer & Explanation

thoumToofwj

thoumToofwj

Beginner2022-05-23Added 16 answers

I just solved the equation with the following method:
( x 2 ) ( x + 1 ) ( x + 6 ) ( x + 9 ) + 108 = 0
( x 2 + 7 x 18 ) ( x 2 + 7 x + 6 ) + 108 = 0
By using the substitution t = x 2 + 7 x we get,
t 2 12 t = 0 t 1 = 0 , t 2 = 12
t 2 12 t = 0 t 1 = 0 , t 2 = 12
So we have,
x 2 + 7 x = 0 x 1 = 0 , x 2 = 7
x 2 + 7 x 12 = 0 x 3 = 7 + 97 2 , x 4 = 7 97 2
Hence x 2 , x 4 ( 1 , 10 )

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