First slide

Theory of equations

Question

$If the sum of two of the roots of x^{3} + p x^{2} + q x + r = 0 is zero, then p q =$

Moderate

A

$- r$
B

$2 r$
C

$- 2 r$
D

$r$

Solution

$\begin{array}{l} Given that, α + β = 0 \\ α + β + γ = - p \Rightarrow γ = - p \end{array}$
$\begin{array}{l} Substituting γ = - p in the given equation \\ \Rightarrow - p^{3} + p^{3} - p q + r = 0 \Rightarrow p q = r \end{array}$

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