Can i get some help with my precalc

so... i dont get this question on a hadnout i got:

Explain why x^4 + 7x^2 + x - 5 = 0 must have a root interval [0,1] , (0≤x≤1)


and this one:

Let "f" be a linear function where f(2) = -5 and f(-3) = 1. State Function f(x)



---
Anyways i dont really get these... i dont know how to solve them please help :) 10pts to best answer

if f(x) = x^4 + 7x^2 + x - 5
it must have a root interval [0,1]
because if you calculate f(0) = -5
and f(1) = +4

that means that the function must cross the x axis between these two values.

in fact you can narrow down the interval to find where the root really is:
f(0)=-5 < 0.5 < f(1)=4
f(0.5)=-2.6875 < 0.75 < f(1)=4
f(0.5)=-2.6875 < 0.625 < f(0.75)=0.0039
f(0.625)=-1.488 < 0.6875 < f(0.75)=0.0039
f(0.6875)=-0.7805 < 0.7188 < f(0.75)=0.0039
f(0.7188)=-0.3982 < 0.7344 < f(0.75)=0.0039
f(0.7344)=-0.1996 < 0.7422 < f(0.75)=0.0039
f(0.7422)=-0.0985 < 0.7461 < f(0.75)=0.0039
f(0.7461)=-0.0474 < 0.748 < f(0.75)=0.0039
f(0.748)=-0.0218 < 0.749 < f(0.75)=0.0039
f(0.749)=-0.009 < 0.7495 < f(0.75)=0.0039
f(0.7495)=-0.0025 < 0.7498 < f(0.75)=0.0039
f(0.7495)=-0.0025 < 0.7496 < f(0.7498)=0.0007
f(0.7496)=-0.0009 < 0.7497 < f(0.7498)=0.0007
f(0.7497)=-0.0001 < 0.7497 < f(0.7498)=0.0007
There is a ZERO at x = 0.7497037224156429

Let "f" be a linear function where f(2) = -5 and f(-3) = 1. State Function f(x)

find the line that goes between these two points:

(2,-5) and (-3,1)

The distance from (2,-5) to (-3,1) is 7.8102
on 6x +5y= -13 or y = -1.2x -2.6
the midpoint is: (-0.5, -2);
the bisector is x -1.2y=1.9 or y =0.8333x -1.5833

you just need to get familiar with these terms.