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Find the product of real roots of x 4 − 2 x 3 + x = 3 8 0
The answer is -20.
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2 solutions
Did you use trial and error to find 5 first and then 4 ? Or is there any specific method to find them ?
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how do we use error to find 5 without a calculator?
No other method other than try and error. Check out useful tips from Niranjan Kanderia here. For those who know me slightly better would know that I use Excel spreadsheet to plot the graph.
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You can use Rational Zero theorem or Synthetic Division in factoring such equation...
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@Dale Angelo Cortez – Why don't you show it. I would like to know how and others may too.
I do not know how to post here lol ,,My head aches due to the brackets,braces etc that are being used on posting.
The product of all roots is 3 8 0 = 2 ⋅ 2 ⋅ 5 ⋅ 1 9 . So if 1 9 is the product of real roots, and roots are integers since coefficient of fourth power is 1 , x = ± 1 , m u s t b e a r o o t . f ( ± 1 ) = 0 . S o t r y 2 , − 2 , 4 , − 4 , 5 , − 5 , f ( ± 2 ) = 0 . f ( 4 ) = 0 . f ( − 4 ) = 0 f ( 5 ) = 0 . p r o d u c t = − 2 0
Yes. 挺好 means very good.
x 4 − 2 x 3 + x − 3 8 0 = ( x − 5 ) ( x 3 + 3 x 2 + 1 5 x + 7 6 ) = ( x − 5 ) ( x + 4 ) ( x 2 − x + 1 9 ) = 0
Therefore, the real roots are − 4 and 5 , and their product is − 2 0 .