If two roots of the equation x3-px2-qx-r-0-r - 0 are equal is magnitude but opposite is sign-

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Domain and Range of Trigonometric Ratios

If two roots ...

Question

If two roots of the equation $x^{3} - p x^{2} + q x - r = 0, (r \neq 0)$ are equal is magnitude but opposite is sign,

p r = q

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q r = p

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p q = r

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Solution

The correct option is C $p q = r$
Given $x^{3} - p x^{2} + q x - r = 0$

Let the roots be $α, - α, β$

Sum of roots $= α - α + β = - \frac{- p}{1}$

$β = p$

Substituting $β$ in given equation

$p^{3} - p^{3} + p q - r = 0$

$p q = r$

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If two roots of the equation x3−px2+qx−r=0,(r≠0) are equal is magnitude but opposite is sign,

The correct option is C pq=rGiven x3−px2+qx−r=0Let the roots be α,−α,βSum of roots =α−α+β=−−p1β=pSubstituting β in given equationp3−p3+pq−r=0pq=r

If two roots of the equation $x^{3} - p x^{2} + q x - r = 0, (r \neq 0)$ are equal is magnitude but opposite is sign,

The correct option is C $p q = r$
Given $x^{3} - p x^{2} + q x - r = 0$

Let the roots be $α, - α, β$

Sum of roots $= α - α + β = - \frac{- p}{1}$

$β = p$

Substituting $β$ in given equation

$p^{3} - p^{3} + p q - r = 0$

$p q = r$