Use the intermediate value therom to show that there is a root of the given equation in the specified interval.
x^5-7=2(25-x); (2,3)
Please explain for understanding and show work, Thank you in advance :)
x^5 - 7 = 50 - 2x
x^5 + 2 x - 57 = 0
y = x^5 + 2 x - 57
if x = 2
y = 32 +4 - 57 = negative number
if x = 3
y = 81*3 + 6 - 57 = positive number
the polynomial is continuous so somewhere in there y was zero