Question

If both x-2 and x-1/2are factor of px^2+5x+r then show that p=r

Answer 1

If both x-2 and x-1/2are factors of px²+5x+r, then 2 and 1/2 are the zeroes of the equation px²+5x+r=0

Substitute x by 2 we get

4p+10+r=0

4p + r = -10 .....(1)

Substitute x by 1/2 we get

p/4 + 5/2 + r =0

p+10+4r=0

p+4r= -10 ......(2)

From (1) and (2)

4p + r = p + 4r

⇒3p = 3r

⇒ p = r

Hence proved