Complex Numbers And Quadratic Equations question 775
Question: If $ x^{2}+2x+2xy+my-3 $ has two rational factors, then the value of m will be [RPET 1990]
Options:
A) $ -6,-2 $
B) $ -6,2 $
C) $ 6,-2 $
D) 6, 2
Show Answer
Answer:
Correct Answer: C
Solution:
Given expression $ x^{2}+2x+2xy+my-3 $ can be written as $ x^{2}+2x(1+y)+(my-3) $ But factors are rational, so $ B^{2}-4AC $ is a perfect square. Now $ 4{ {{(1+y)}^{2}}-(my-3) }\ge 0 $
Þ $ 4{ y^{2}+1+2y-my+3 }\ge 0 $
Þ $ y^{2}+2y-my+4\ge 0 $ Hence $ 2y-my= \pm 4y $ {as it is perfect square}
Þ $ 2y-my=4y\Rightarrow m=-2 $ . Now taking (+) sign, we get $ m=6 $ .
BETA
