Question
Asked Nov 24, 2019
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#8a using Descartes's rule of sign

8. Verify the following assertions.
If all the coefficients of an equation are positive
(a)
and the equation involves no odd powers of x,
then all its roots are imaginary.
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8. Verify the following assertions. If all the coefficients of an equation are positive (a) and the equation involves no odd powers of x, then all its roots are imaginary.

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Expert Answer

Step 1

Prove in the following that if all the coefficients of an equation are positive and the equation involves no odd powers of x, then all its roots are imaginary.

Step 2

Take an equation,

f(2) - аx* +ах +а,* +.+
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f(2) - аx* +ах +а,* +.+

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Step 3

There is no sign change between all the terms. Therefore, there is no positiv...

f(-x)=a(-x)a (-x)+a (-x)+
6
22
+ q (-x)
- ax + аx* + ад+.
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f(-x)=a(-x)a (-x)+a (-x)+ 6 22 + q (-x) - ax + аx* + ад+.

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