Question

If (x-1/2) and (x-2) are factors of
px²+5x+r then prove that p=r

Answer 1

I hope this answer will be helpful to you

Answer 2

(x-2) is a factor

⇒ x = 2

⇒ 2 is a root of the polynomial

px²+5x+r=0

p(2)²+5(2)+r=0

4p+10+r = 0 -------(1)

now,

since 1/2 is also a factor,

⇒ p(1/2)²+5(1/2)+r = 0

⇒p/4+5/2+r = 0

⇒ (p+10)/4 +r =0

⇒(p+10+4r)/4=0

⇒p+10+4r =0 -------(2)

from equating (1) and (2)

4p+10+r = p+10+4r

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

3p - 3r =0

3(p-r) = 0

p-r =0

p=r