if both (x-2)and(x-1/2)are factors of px2+5x+r.show that p=r

Asked by  | 29th Sep, 2013, 01:03: PM

Expert Answer:

Let f(x) = px2 + 5x + r
(x - 2) is a factor of f(x), so f(2) = 0
=> 4p + 10 + r = 0           ... (1)
 
Also, (x - 1/2) is a factor of f(x) so f(1/2) = 0
=> p/4 + 5/2 + r = 0
=> p + 10 + 4r = 0           ... (2)
Subtracting (2) from (1), we get,
3p - 3r = 0
or, p = r

Answered by  | 29th Sep, 2013, 01:13: PM

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