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Roots of a Quadratic Equation

The roots of ...

Question

The roots of the quadratic equation $(x + β) (x - α) = 0$ are:

A

$α, β$

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B

$β, - α$

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C

$α, - β$

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D

$- α, - β$

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Solution

The correct option is C
$α, - β$

Observe that the equation is already factorized and we also know that the root of an equation is that value which satisfies the equation.
Since a product of two factors would be zero when either of the factors is zero [or both of them zero], we shall equate the factors to zero.
$(x + β) (x - α) = 0$
which means, $(x + β) = 0 o r (x - α) = 0$
$x = - β o r x = α$
The roots of given equation are $α, - β$ .

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