Complex Numbers And Quadratic Equations question 665
Question: Let $ a>0,b>0 $ and $ c>0 $ . Then both the roots of the equation $ ax^{2}+bx+c=0 $
Options:
A) are real and negative
B) have negative real parts
C) are rational numbers
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ a>0,b>0,c>0 $ Given equation $ {ax^{2}} + bx + c = 9 $ we know that $ D = b^{2} - 4ac $ and $ x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a} $ Let $ {b^{2}}-4ac>0,b>0 $ If $ a > 0, c > 0 then b^{2} - 4ac < b^{2} $
$ \Rightarrow $ Roots are negative Let $ {b^{2}}-4ac<0 $ , then $ x=\frac{-b\pm i\sqrt{4ac-b^{2}}}{2a} $ roots are imaginary and have negative real part. $ ( \because b>0 ). $
BETA
