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

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4-2.Quadratic Equations and Inequations

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

A

$-r$

B

$r$

C

$2\ r$

D

$-2\ r$

Solution

(b) Given that, $\alpha + \beta = 0$

$\alpha + \beta + \gamma = – p \Rightarrow \gamma = – p$

Substituting $\gamma = – p$in the given equation

==> $ – {p^3} + {p^3} – pq + r = 0 \Rightarrow pq = r$.

Standard 11

Mathematics

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