Question

Given f(x)=9x^8+2x^5-8x-3, how many sign changes are there in the coefficients of f(-x?A.3B.2C.1D.0

Answer 1

Given:

$f\mleft(x\mright)=9x^8+2x^5-8x-3$

Now, define f(-x),

$\begin{gathered} f\mleft(-x\mright)=9(-x)^8+2(-x)^5-8(-x)-3 \\ f(-x)=9x^8-2x^5+8x-3 \end{gathered}$

It is observed that,

$+9\text{ -2 +8 -3 }$

There are three sign changes. First from + to - , then - to + and lastly + to -.

Answer: option A)