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in Mathematics by (80.8k points)

If p, q are the zeroes of the polynomial f(x) = x2 + k(x - 1) - c, then (p - 1)(q - 1) is equal to ......

(A) c - 1 

(B) 1- c

(C) c 

(D) 1 + c

1 Answer

+1 vote
by (52.5k points)
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Best answer

The correct option is: (B) 1- c

Explanation:

Given equation is x2 + k(x- 1) - c

= x2 + kx - (k + c)

Since, p and q are the zeroes,

... p + q = -k and pq = -(k+ c)

Now, (p - 1) (q - 1) = Pq - q - p + 1

= pq - (p + q)+ 1 = -(k+ c)-(-k) + 1

= -k - c + k + 1 = 1 - c

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