If both (x-2)and(x-1/2)are factors of px2+5x+r.show that p=r

CBSE Class 9
1

If both (x-2)and(x-1/2)are factors of px2+5x+r.show that p=r

2

Let f(x) = px2 + 5x + r
(x - 2) is a factor of f(x), so f(2) = 0
⇒ 4p + 10 + r = 0 … (1)
Also, (x - 1/2) is a factor of f(x) so f(1/2) = 0
⇒ p/4 + 5/2 + r = 0
⇒ p + 10 + 4r = 0 … (2)
Subtracting (2) from (1), we get,
3p - 3r = 0
or, p = r