Question

The value -1 is a lower bound for the zeros of the function shown below.

f(x)=x^4+x^3-11x^2-9x+18

A. True
B. False

Answer 1

can we use calculus?

Answer 2

yes

Answer 3

FALSE

x=-3,-2,1,3 are roots of polynomial
i was trying to find a proof. i found all of roots!!!!!!:D

by letting x=-(t+1)
u will have
\[t^4+3t^2-8t^2-12t+16=t^4-8t^2+16+3t^3-12t=(t^2-4)^2+3t(t^2-4)\\=(t^2-4)(t^2+3t-4)=(t-2)(t+2)(t-4)(t+1)\]

Another way
u can prove it by Mean Value Theorem
f(-1)>0 and f(-2.5)<0 so there is a root on the interval (-2.5 , -1)

Answer 4

oh ok thank you!! :)

Answer 5

welcome dear:D