Question

if both x-2 and x-1\2 are factors of px^2+5x+r then find the other factors​

Answer 1

Answer:

Given, f(x) = px^2+5x+r and factors are x-2, x-1/2

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.

Hope this helps!