First slide

Theory of equations

Question

If the roots of the given equation $(m^{2} + 1) x^{2} + 2 amx + a^{2} - b^{2} = 0$ be equal, then

Moderate

A

$a^{2} + b^{2} (m^{2} + 1) = 0$
B

$b^{2} + a^{2} (m^{2} + 1) = 0$
C

$a^{2} - b^{2} (m^{2} + 1) = 0$
D

$b^{2} - a^{2} (m^{2} + 1) = 0$

Solution

Roots are equal, then $B^{2} - 4 AC = 0$
$\Rightarrow 4 a^{2} m^{2} = 4 (m^{2} + 1) (a^{2} - b^{2})$
$\Rightarrow a^{2} - b^{2} (m^{2} + 1) = 0 .$

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