There is a solution to x5−2x3−2=0 between x=0 and x=2
- T
There is a solution to x5−2x3−2=0 between x=0 and x=2
- T
The correct option is A T
This is an application of intermediate value theorem. When we are given a function and told a statement about roots or some values between boundaries, we should be checking if theorem’s like Rolle’s theorem, intermediate value theorem or LMVT is applicable there. To check if IVT is applicable, we will substitute the value x = 0 and 2 in the given equation
When x = 0, we get f(x) = -2 and when x = 2, we get f(x) = 14
Since the given function is a polynomial, we can say that it is continuous.
The value of the function at x = 0 and 2 are -2 and 14. According to IVT, there should be at least one point where the function takes the value zero(zero is between -2 and 14) in the interval (0,2).
This is clear from the figure given below. So, the given statement is correct. One important point to note here is that there could be more than one point where the function becomes zero for some functions
This is an application of intermediate value theorem. When we are given a function and told a statement about roots or some values between boundaries, we should be checking if theorem’s like Rolle’s theorem, intermediate value theorem or LMVT is applicable there. To check if IVT is applicable, we will substitute the value x = 0 and 2 in the given equation
When x = 0, we get f(x) = -2 and when x = 2, we get f(x) = 14
Since the given function is a polynomial, we can say that it is continuous.
The value of the function at x = 0 and 2 are -2 and 14. According to IVT, there should be at least one point where the function takes the value zero(zero is between -2 and 14) in the interval (0,2).
This is clear from the figure given below. So, the given statement is correct. One important point to note here is that there could be more than one point where the function becomes zero for some functions
