Descartes' Rule of Signs

[jaydstar23]

:?: If Q(x)=-P(x), do P(x) and Q(x) have the same zeros?

 

[stapel]

Consider Q(x) in factored form.

. . . . .m(x - a₁)(x - a₂)....(x - a_n) = Q(x)

Now multiply through by -1 to get P(x). Set equal to zero.

Will you get any different values for the zeroes?

Eliz.

 

[Matt]

:?: If Q(x)=-P(x), do P(x) and Q(x) have the same zeros?

Let c be a zero of P(x). Then $\displaystyle Q(c)=-P(c)=-0=0.$

Let c be a zero of Q(x). Then $\displaystyle P(c)=-Q(c)=-0=0.$

 

[jaydstar23]

:lol: Thank you! Seems simple after seeing your replies!