Question

help me in finding the answer of this

Answer 1

In first case,
(x-2) is a factor so, x-2 = 0
x = 2

px^2 + 5x + r = 0
p2^2 + 5(2) + r = 0
4p + 10 + r = 0
4p + r = -10............eq (1)

In second case,
(x-1/2) is a factor so, x-1/2 = 0
x = 1/2

px^2 + 5x + r = 0
p(1/2)^2 + 5(1/2) + r = 0
1/4 p + 5/2 + r = 0

Multiplying 4 on both sides,
p + 10 + 4r = 0
p + 4r = -10...........eq (2)

eq (1) - eq (2), we get,
3p - 3r = 0
3p = 3r
p = r

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