Statement-1 : The equation `3x^(5)+15x-18=0` has exactly one real root.
Statement-2: Between any two roots of , there is a root of its derivative f'(x) .

Options

A. Statement-1 is True, Statement-2 is Ture, Statement-2 is a correct explanation for statement-1
B. Statement-1 is True, Statement-2 is Ture, Statement-2 is not a correct explanation for statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 True.

Answer

A

Explanation

Statement-, being algebraic intepretition of Rolle's theorem, is true,
Let `x_(1),x_(2)` be two roots of `f(x)=3x^(5)+15x-18`. Then `f'(x)=12x^(4)+15` must have a root between `x_(1) and x_(2)` . But, `f(x)le0` for all x, So, it has no real root. This contradicts the algebraic interpertaion of Rolle's theorem.
Hence `f(x)=3x^(5)+15x-18` has exactly one real root x=1
Thus, both the satement are true and statement-2 is correct explanation for statement-1