First slide

Theory of equations

Question

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

Moderate

A

$- r$
B

$r$
C

$2 r$
D

$- 2 r$

Solution

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

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