Respuesta :
Answer:
a) -5/2.
Step-by-step explanation:
Try substituting (-5/2) into f(x):
6(-5/2)^4 + 5(-5/2)^3 - 33(-5/2)^2 - 12(-5/2) + 20
= 234.375 + -78.125 - 206.25 + 30 + 20
= 0.
So it is -5/2.
Answer:
a) [tex]x= -5/2[/tex]
Step-by-step explanation:
We substitute in the function the values given in the options to confirm whether they are roots or not
a) [tex]x= -5/2[/tex]
the function will be:
[tex]f(-\frac{5}{2} )=6(-\frac{5}{2} )^4 + 5(-\frac{5}{2} )^3-33(-\frac{5}{2} )^2-12(-\frac{5}{2})+20[/tex]
simplifying:
[tex]f(-\frac{5}{2} )=6(\frac{625}{16} )-5(\frac{125}{8} )-33(\frac{25}{4} )+30+20[/tex]
[tex]f(-\frac{5}{2} )=234.375-78.125-206.25+50\\f(-\frac{5}{2} )=0\\\\[/tex]
since the function when [tex]x= -5/2[/tex] is equal to zero, this is an actual root of f(x).
