# 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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#8a using Descartes's rule of sign help_outlineImage Transcriptionclose8. 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. fullscreen
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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,

Step 3

There is no sign change between all the terms. Therefore, there is no positiv... help_outlineImage Transcriptionclosef(-x)=a(-x)a (-x)+a (-x)+ 6 22 + q (-x) - ax + аx* + ад+. fullscreen

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