NDA2024MathematicsQuadratic EquationActual
If f(x)=9 x-8 x such that g(x)=f(x)-1 , then which one of the following is correct?
Options
- Ag(x)=0 has no real roots
- Bg(x)=0 has only one real root which is an integer
- Cg(x)=0 has two real roots which are integers
- Dg(x)=0 has only one real root which is not an integer
Correct answer
B. g(x)=0 has only one real root which is an integer
Step-by-step solution
Given, f(x)=9 x-8 x , g(x)=9 x-8 x -1 Lets take x = t ^2 , aligned & g (t^2 )=9 t^2-8 t-1 & t= 8 10 18 t= 18 18 or -1 9 & t=1 or -1 9 & x=1, 1 81 aligned g(x)=0 has only one real root which is an integer.