Question

If both x-2 and x - 1/2 are factors of px²+5x+r, then
A. p = r
B. p + r = 0
C. 2p + r = 0
D. p + 2r = 0

Answer 1

Answer:

A is correct

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Answer 2

Given: Both x - 2 and x - ½  are factors of px² + 5x + r.  

Let f(x) = px² + 5x + r  

Since, x - 2 and x - 1/2 are factors of f (x)

∴  f (2) = 0 and f(1/2) = 0

On Substituting x = 2 in f (x),

= p(2)² + 5 × 2 + r = 0  

= p × 4 + 10 + r = 0

=  4p + 10 + r = 0   ………... (1)

On Substituting x = ½  in f (x),

= p(½ )² + 5 × 1/2 + r = 0  

= p × ¼ + 5/2 + r = 0

= p/4 + 5/2 + r = 0

p + 10 + 4r = 0  

p + 4r = - 10…………..  (2)

On solving eq (1) and (2) :  

4p + r = -10 and p + 4r = - 10

4p - p - 10 + 10 = 4r - r

3p = 3r    

p = r

Hence proved.

Among the given options option (A) p = r is correct.

HOPE THIS ANSWER WILL HELP YOU…..

 

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