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

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

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»

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