Question

if both x-2 and x-1/2 are factors of px^2+5x+r

Answer 1

x-2 and x-1/2 are factors of px²+5x+r then put x=2 nd 1/2.
when x=2 thn equation will be 4p + r = -10.....(.1)
nd when x=1/2 thn equation will be p/4+r= -5/2
multiply this eqn by 4 u will get p+4r= -10........(2)
slve eqn (1)nd(2) u will get -15r=30.then r= -2

Answer 2

p [x] = px^2 + 5x + r

p[2] = 0

p*2^2 + 5*2+r = 0

4p +10+ r =0 ___________ 1

p[1/2] =0

p*[1/2]^2 *5*1/2 + r =0

p/4 +5/2+r =0

multiplying 4 to both side

4*p/4 +4*5/2+4*r = 0*4

p + 10+ 4r = 0 ______________2

subtract 2 - 1

4p + 10 + 4r =0 - p -10 +4x = 0

ans 3p - 3r =0

3p -3r

= p/r = 3/3 p/r = 1