if x^2-ax+2a+5=0 is a perfect square,then find the value/s of a.

Asked by  | 15th Nov, 2012, 11:05: AM

Expert Answer:

Given, x2-ax+2a+5 is a perfect square. So, it will be of the form (x - t)2, where t is a constant.
x2-ax+2a+5 = (x - t)2
x2-ax+2a+5 = x2 - 2xt + t2
Comparing both sides, we get,
-ax = -2xt 
So, a = 2t
Also, 2a+5 = t2
4t + 5 =  t2
 t2 - 4t - 5 = 0
(t + 1) (t - 5) = 0
t = -1 or 5
So, a = -2 or 10

Answered by  | 15th Nov, 2012, 11:16: PM

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