Complex Numbers And Quadratic Equations question 27
Question: The adjoining figure shows the graph of $ y=ax^{2}+bx+c $ . Then
Options:
A) $ a<0 $
B) $ b^{2}<4ac $
C) $ c>0 $
D) a and b are of opposite signs
Show Answer
Answer:
Correct Answer: A
Solution:
It is evident from the figure that the function $ y=ax^{2}+bx+c $ has a maximum between $ x_1 $ and $ x_2 $ .
$ \therefore \frac{d^{2}y}{dx^{2}}<0\Rightarrow $ $ a<0 $ Obviously, $ x_1,x_2>0 $
Þ $ x_1+x_2>0 $
Þ Sum of the roots > 0
Þ $ \frac{-b}{a}>0\Rightarrow \frac{b}{a}<0 $
Þ a and b are of opposite signs.
BETA
