SOLUTION: Please help me solve this question: Show that the equation has at least one real root. a) cosx=x^3 b)x^(5)-x^(2)+2x+3=0

Question 734675: Please help me solve this question:
Show that the equation has at least one real root.
a) cosx=x^3
b)x^(5)-x^(2)+2x+3=0
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
a) Consider
It is a continuous function.

The continuous function is positive for and negative for so it must have a zero somewhere in the (0,) interval (according to the intermediate value theorem).

You could do something similar with .
You can easily see that and and that is as much as is needed to prove is that there is one real root.
RELATED QUESTIONS
please a need help with this QUESTION (a)prove that the equation mx(x^2+2x+3) =... (answered by KMST)

f(x)=x^5-6x^4+11x^3-2x^2-12x+8 has (x-2) as a factor determine which one of the... (answered by MathLover1,Edwin McCravy)

Please help me answer this question: Show that for all real values of 'a' greater than 4. (answered by josgarithmetic)

please help me understand and solve the equation x^3 + 2x^2 + x + 2 = 0, if -2 is a... (answered by jim_thompson5910)

Please help me with this and show the work. Give the equation of a function that has... (answered by rfer)

Please help me I am so lost. Please show all steps and work. Thanks Real Zeros of... (answered by Alan3354,Theo)

I will really appreciate if you guys help me with these questions. Thank you so much.... (answered by ewatrrr)

please help me solve this 1. prove the identity sinx/1-cosx =1/tanx 2. hence solve... (answered by Alan3354)

Please help me solve this equation: The quadratic equation {{{ (b-c)x^2+(c-a)x+(a-b)=0... (answered by math_helper)