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 andge; 2. Which one of the following is correct?a)(k + 1)2p2= kqb)(k + 1)2q = kp2c)k2q = (k + 1) p2d)k2p2= (k + 1)2qCorrect answer is option 'B'. Can you explain this answer?

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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?

a)
(k + 1)²p² = kq
b)
(k + 1)²q = kp²
c)
k²q = (k + 1) p²
d)
k²p² = (k + 1)²q

Correct answer is option 'B'. Can you explain this answer?

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Let p and q be non-zero integers. Consider the polynomial A(x) = x2+ p...

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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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?a)(k + 1)2p2= kqb)(k + 1)2q = kp2c)k2q = (k + 1) p2d)k2p2= (k + 1)2qCorrect answer is option 'B'. Can you explain this answer?

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