i) Find the range of K for which f(x) is positive for all real x.
ii) For what values of K does the equation f(x) = 0 have two equal real roots.
iii) If the roots f(x) = 0 are real and if the difference of the roots is equal to 292
(2 square root 92)
i) find the x where f(x) has the min value:
df/dx = 0 ====> 2x-2(1+3k)=0 ====> x=1+3k
so, the question can be made : find k to make f(1+3k)>0
ii)to have two equal real roots:
g(k)=4(1+3k)^2-4*7(3+2k)=0
iii)the difference of the two roots = 2 times the root of g(k), where g(k) is the same in ii)