Need help to solve this

[isuranja]

Question is,

Let K is real and f(x) = x² - 2(1+3K)x + 7(3+2K)

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 292
(2 square root 92)

Please help me on this get correct answers.

Regards,
Isuranja

 

[wholx]

not very tough.

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)

 

[justin999]

it is too ease, it can be solved with the method learned in high school,
b2-4ac<0
b2-4ac=0

 

[whynot910]

what justin999 is right, this kind of problems can be solved by high schcool algebra knowledge.