First slide

Theory of expressions

Question

If the roots of the equation $a x^{2} + b x + c = 0$ are real and distinct, then

Moderate

A

both roots are greater than $\frac{- b}{2 a}$
B

both roots are less than $\frac{- b}{2 a}$
C

one of the roots exceeds $\frac{- b}{2 a}$
D

none of these

Solution

The roots of the given equation are
$α = \frac{- b - \sqrt{b^{2} - 4 a c}}{2 a} and β = \frac{- b + \sqrt{b^{2} - 4 a c}}{2 a}$
Since $α, β$ are real and distinct, therefore $b^{2} - 4 a c > 0$
It is evident from Fig 1 that $β_{1} < - \frac{b}{2 a} < α$
So, one root is less than - $\frac{b}{2 a}$ and other exceeds - $\frac{b}{2 a}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App