Question

if x-2 and2x-1 are factors of px^2+5x+r show that p=r

Answer 1

Given that (x - 2) and (2x - 1) are factors,

So, x - 2 = 0       and   2x - 1 = 0    
      x = 2             and  x = 1/2 

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Putting x = 2

px² + 5x + r = 0 

p(2)² + 5(2) + r = 0 

4p + 10 + r = 0 

4p + r = -10      -------1equation

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Putting x = 1/2 

p(1/2)² + 5(1/2) + r = 0 

p/4 + 5/2 + r = 0 

(p + 4r)/4 = -5/2 

p + 4r = -10  ----------2equation

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4p + r = -10 
p + 4r = -10 


As both are equal to -10 

then ,equations are equal



4p + r = p + 4r  

3p - 3r = 0 

3(p - r) =  0 

p  - r =0/3 

p - r =0 

p =r 


Hence, proved.



i hope this will help you


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