First slide

Theory of equations

Question

If $A = {x : f (x) = 0}$ and $B = {x : g (x) = 0},$ then $A \cap B$ will be the set of roots of the equation

Moderate

A

${f (x)}^{2} + {g (x)}^{2} = 0$
B

$\frac{f (x)}{g (x)}$
C

$\frac{g (x)}{f (x)}$
D

none of these

Solution

Let $α \in A \cap B .$ Then ,

$\Rightarrow α \in A$ and $α \in B$
$\Rightarrow f (α) = 0$ and $g (α) = 0$
$\Rightarrow [f (α)]^{2} + [g (α)]^{2} = 0$
$\Rightarrow α$ is a root of $[f (x)]^{2} + [g (x)]^{2} = 0$

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