If both x-2 and x-1/2 are the factors of px^2+5x+r. Show that p=r

1.	If both x-2 and x-1/2 are the factors of px^2+5x+r. Show that p=r
Answer» Given, f(x) = px^2+5x+r and factors are x-2, x-1/2Substitute x = 2 in place of equation, we get= p2^2+52+r=0 = 4p + 10 + r = 0 ------------ (i)Substitute x = 1/2 in place of equation. \xa0p/4 + 5/2 + r = 0\xa0p + 10 + 4r = 0 ------------------- (ii)On solving (i),(ii) we get4p+r=-10 and p+4r+10=04p+r=p+4r3p=3r p = r.

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