Equation

[Yunie]

Given that x = 1 1/2 is the only solution to the equation 4x^2 - ax + b = 0, find the value of a and of b.

Please show and explain your workings, thanks a lot!

[zaza]

What does a generic quadratic look like when factorised? What must be true if there is only one root? What do you get when you expand out of the brackets?

[Yunie]

Haha...I don't know how to answer your above 3 questions cos I don't really understand...so that's why I could not solve or understand this problem...

But still, below is the working solution from my assignment book and I really wish you could explain it to me cos I don't really understand why the question is done in that particular way. Thanks.



Here is the working solution from my assignment book but I don't really understand...

Since x = 1 1/2 is the only solution, the eqn is a perfect square.

--> (2x - 3)^2 = 0
4x^2 - 12 + 9 = 0

By comparison, a = 12, b = 9


So, from the working solutions, does it mean that since x = 1 1/2, it has to be a perfect square? I don't understand...hmm...

[opus]

For quadratic equations in the form of:
0= x^2 +px +q
The two possible solutions for x are (using the so called pq-formula):

x1= -p/2 + squareroot( (p/2)^2 -q)
x2= -p/2 - squareroot( (p/2)^2 -q)

In your case there shall be only one solution, in this case the squareroot-part has to be 0. But this can only be true if (p/2)^2=q.
I hope you can take from here!

[krtxmrtz]

Haha...I don't know how to answer your above 3 questions cos I don't really understand......

I think zaza means you're not going to get too far if you don't understand the theory.