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Multiple Choice Questions

If x k is the HCF of x2 ax b and x2 cx d then what is the value of k ........

Quantitative Aptitude (CPO) Algebra

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If (x + k) is the HCF of (x² + ax + b) and (x² + cx + d), then what is the value of k?

b + d /a + c

b + d /c + d

a – b /c – d

b - d /a - c

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Explanation:

Given that, (x + k) is the HCF of (x² + ax + b) and (x² + cx + d),
i.e., (x + k) is a factor of both expression
Let f(x) = (x² + ax + b) and g(x) = (x² + cx + d)
Now, f(x) = g(x) at (x = –k)
⇒ (–k)² + a(–k) + b = (–k)² + c (–k) + d
⇒ (a – c)k = (b – d)
⇒ k = (b – d) /(a – c)