Question

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

Answer 1

Let, f(x)=px^2+5x+r; (x-2=0)
       f(2)=p*(2)^2+5*2+r ; (x=2)
       0=p*4+10+r
       -10=4p+r
        4p+r=-10
Let, f(x) =px^2+5x+r; (x-1/2=2)
       f(1/2)=p(1/2)*2+5*1/2+r;(x=1/2)
        0=p*1/4+5/2+r
        0=p/4+5/2+r
        -5/2=p/4+r
          p/4+r=-5/2
          p/4+r/1=-5/2
         (p+4r)/4=-5/2
          p+4r=-20/2(By cross multiplication)
           p+4r=-10    

4p+r=-10(i)*1

p+4r=-10(ii)*4

 

4p+r=-10

4p+16r=-40

(-)   (-)  (+)

     -15r=30           

      15r=-30  

  r=-30/15

r=-2

4p+r=-10

4p-2=-10

4p=-10+2

4p=-8

p=-8/4

p=-2

Since, p=-2

           r=-2

Therefore, p=r