carcass wrote:
If there is exactly one root of the equation x^2 + ax + b, where a and b are positive constants, what is b in terms of a?
A. a/2
B. a
C. 3a/2
D. a^2/2
E. a^2/4
I'm not sure how to solve this problem. It take me almost five minutes of brainstorming but nothing.
The only thing on how I 'm triyng to attack the same is : (x+b)^2 whre the only root is x=-b.
![:(]( "Sad")
A. a/2
B. a
C. 3a/2
D. a^2/2
E. a^2/4
I'm not sure how to solve this problem. It take me almost five minutes of brainstorming but nothing.
The only thing on how I 'm triyng to attack the same is : (x+b)^2 whre the only root is x=-b.
Procedure 1:
only one root, but x^2 indicates there must be two roots. so two root are equal = x
now, x+x = -a
or, x = -a/2
And x.x= b
or, x^2 = b
or, a^2/4 = b (so (E) answer)
procedure 2: (the standard equation for all the equation that have the highest power that is 2, is below=
x^2 - (addition of two root)x + (multiplication of two roots) = 0
now compare it with
x^2 + ax + b
or, x^2 - (-a/2 - a/2)x+ (-a/2)(-a/2) = 0
so, b = a^2 /4