college algebraneed help please!!
posted by ladybug .
use the intermediate value theorem to show that the polynomial function has a zero in the given interval.
f(x)=x^5x^4+9x^35x^216x+5;[1.3,1.6]
f(x)1.3= ? simplify answer
f(x)1.6= ? "

1.3^5 = 3.71293> 3.71
1.3^4 = 2.8561 >2.86
1.3^3 = 2.197 >19.77
1.3^2 = 1.69>8.45
16*1.3 >20.8
+5 > +5
add
f(1.3) = 3.63
now do f(1.6)
1.6^5 = 10.48576 > 10.5
1.6^4 = 6.5536 >6.55
1.6^3 = 4.096 > 36.9
1.6^2 = 2.56 >12.8
1.6*16 >25.6
+5>+5
add
f(1.6) = 7.45
ah ha!
somewhere in between there this function which is continuous crossed the x axis at least once to get from 3.63 to + 7.45
Therefore it had at least one zero in there.