Complex Numbers And Quadratic Equations question 188
Question: The value of ? $ c $ ?for which $ |{{\alpha }^{2}}-{{\beta }^{2}}|=\frac{7}{4} $ , where $ \alpha $ and $ \beta $ are the roots of $ 2x^{2}+7x+c=0 $ , is
Options:
A) 4
B) 0
C) 6
D) 2
Show Answer
Answer:
Correct Answer: C
Solution:
We have $ \alpha +\beta =-\frac{7}{2} $ and $ \alpha \beta =\frac{c}{2} $ \ $ |{{\alpha }^{2}}-{{\beta }^{2}}|=\frac{7}{4}\Rightarrow {{\alpha }^{2}}-{{\beta }^{2}}=\pm \frac{7}{4} $
Þ $ (\alpha +\beta )(\alpha -\beta )=\pm \frac{7}{4} $
Þ $ -\frac{7}{2}\sqrt{\frac{49}{4}-2c}=\pm \frac{7}{4} $
Þ $ \sqrt{49-8c}=\mp 1\Rightarrow 49-8c=1\Rightarrow c=6 $
BETA
