Paragraph: Let Question: Let y=g(x) be a twice differentiable function such that g( )=0, g( )=2, g( )=-3 , g(a)=5, g(b)=0 , then number of minimum distinct real roots of the equation (g^ (x) )^2+g(x) g^ (x)=0 in [1,14] is:

Step-by-step solution

aligned & f(x)=x^3-a x^2+b x-8 & =2 and b=2 a & = 2 p and =2 p ( p is the common ratio) & I p=-1,1,2,-2 & =-2,2,1,-1 ; =2,2,2,2 ; =-2,2,4,-4 & =1, =2, =4 and a=7 ; b=14 aligned Roots of the equation f(x- )=0 are + , 2 , + which are in H.P.