Question

If both x-2 and 2x-1 are factor 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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