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If (x + k) is the common factor of \( x^2 + ax + b \) and \( x^2 + cx + d \), then what is k equal to ?

A) (d - b)/(c - a)
B) (d - b)/(a - c)
C) (d + b)/(c + a)
D) (d - b)/(c + a)

Correct Answer:

A) (d - b)/(c - a)

Description for Correct answer:

Here (x + k) is common factor of \( \Large x^{2} + ax +b \) and \( \Large x^{2} + cx + d \)

Putting x = -k in \( \Large x^{2} + ax +b \),

We get \( \Large (-k)^{2} + a(-k) + b = 0 \)

\( \Large k^{2} - ak + b = 0 \) ... (i)

and putting x = -k in \( \Large x^{2} + cx + d \),

we get \( \Large (-k)^{2} +c(-k)+d=0 \)

\( \Large k^{2} - ck + d = 0 \) .... (ii)

From equation (i) and (ii) we get

\( \Large k^{2} - ak + b =k^{2}-ck +d \)

-ak + ck = d-b

\( \Large k = \frac{d - b}{c - a} \)

Option (A)is correct.

Part of solved CDS Maths(1) questions and answers : Exams >> CDSE >> CDS Maths(1)

Comments

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