Question

if both (x-2) and (x-1/2)are factor of polynomials px^2+5x+r,show that p/r=1.

Answer 1

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First condition,

$x = 2$

Substitute in the equation,

$p(2)^2 + 5(2) + r = 0$

$4p + 10 + r = 0---(2)$

Similarly, second condition

$x = 1/2$

Substitute,

$p(1/2)^2 + 5(1/2) + r = 0$

$1/4p + 5/2 + r = 0$

Multiply throughout by 4,

$p + 10 + 4r = 0---(2)$

Now equate (1) and (2),

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

$3p - 3r = 0$

$p - r = 0$

$p = r$

Hence,

$p/r = 1$