Question

If both x- 1 and 2x-1 are factors of px square +5 x+ r, show that p= r.

Answer 1

Its not (x-1), it should be (x-2)............
Given, f(x) = px^2+5x+r and factors are (x-2), (x-1/2) [ (2x-1) = (x-1/2) ] divide by 2

Substitute x = 2 in place of equation, we get
= p*2^2+5*2+r=0
= 4p + 10 + r = 0 ------------ (i)

Substitute x = 1/2 in place of equation.
p/4 + 5/2 + r = 0
p + 10 + 4r = 0 ------------------- (ii)

On solving (i),(ii) we get
4p+r=-10 and p+4r+10=0
4p+r=p+4r
3p=3r
p = r.