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Let p and q be non-zero integers. Consider the polynomial A(x) = x2 + px + q. It is given that (x - m) and (x - km) are simple factors of A(x), where m is a non-zero integer and k is positive integer, k ≥ 2. Which one of the following is correct?

Let p and q be non-zero integers. Consider the polynomial A(x) = x2 + px + q. It is given that (x - m) and (x - km) are simple factors of A(x), where m is a non-zero integer and k is positive integer, k ≥ 2. Which one of the following is correct? Correct Answer (k + 1)<sup>2</sup>q = kp<sup>2</sup>

If (x - m) and (x - km) are the factors of the polynomial, then m and km are roots of the polynomial

Sum of roots = -b/a

m + km = -p

m(k + 1) = -p       ---- (1)

Product of roots = c/a

m × km = q

km2 = q       ---- (2)

Divide equation (2) by square of equation (1)

 (k + 1)2/k = p2/q

∴ (k + 1)2q = kp2

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