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f(x) = x(squared) + kx + (k+3) where k is a constant. Given that the equation f(x) = 0 has qual roots..
A) Find the possible values of k
B) Solve f(x) = 0 for each possible value of k
Given instead that k = 8
C) Express f(x) in the form (x + a)squared + b, where a and b are constants.
D) Solve f(x) = 0 giving your answers in surd form
should that be "equal roots"?Quote:
Originally Posted by cougar
if so, then
you need the discriminant to be zeroQuote:
A) Find the possible values of k
B) Solve f(x) = 0 for each possible value of k
this is asking you to complete the square, do you know how to do that? (you can google it :D)Quote:
Given instead that k = 8
C) Express f(x) in the form (x + a)squared + b, where a and b are constants.
use the quadratic formula. do you remember it?Quote:
D) Solve f(x) = 0 giving your answers in surd form
Sorry to ask, but I couldn't find anywhere what a 'qual root' is.
About (C): if k=8, then
Now you must use the fact that, which is a particular case of Newton's Binomial. If you examine the expression for f(x), you can see that taking a = x and b = 4 and applying it to (I) seems promising. In fact:
Notice that it's not f(x) yet, but it's close. All you need to do now is adding 8:
And this answers your questions, a = 4 and b = 8. The name of this procedure is Square Completion. Check the link for further examples.
For (D), I'll leave it to you with a tip: does what you just did in (C) helps you to find the roots? Or inform you whether they exist in?
Regards,
Yeh oops a typo, supposed to be equal. Thanks for the help YOU RULE :D