Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Let $\alpha$ and $\beta(\alpha>\beta)$ be roots of the quadratic equation $ax ^2+ bx + c =0$.
If $0< a < c$ and $a + c = b$, then which of the following statement(s) is/are correct?

Complex Numbers and Quadratic Equations

Solution:

$ \text { Given } \alpha>\beta ; 0< a < c \Rightarrow a >0, c >0 \text { and } c > a $
$\text { an } {a}- b + c =0 \Rightarrow f (-1)=0 \Rightarrow x =-1 \text { is one root. }$
image
and product of root $=\frac{ c }{ a }>1$
Hence the other root must also be less than -1
$\Rightarrow $ larger root is -1 .
image
Also, $(-1)(\alpha)=\frac{ c }{ a } \Rightarrow$ smaller root $=\frac{- c }{ a }$.
As sum of roots $=\frac{-b}{a}<0 \Rightarrow b>0$.