Question

If (x + k) is the HCF of ax² + ax + b and x² + cx + d, then what is the value of k ?

(a) \(\frac{b+d}{a+c}\) 

(b) \(\frac{a+b}{c+d}\)

(c) \(\frac{a-b}{c-d}\)

(d) None of these

Answer 1

(d) None of these

Hint. 

ak² – ak + b = 0

k² – ck + d = 0 

Solving by the rule of cross multiplication,

\(\frac{k^2}{-ad+bc}\) = \(\frac{k}{b-ad}\) = \(\frac{1}{-ac+a}\)

⇒ k = \(\frac{b-ad}{a(1-c)},\frac{bc-ad}{b-ad}.\)