First slide

Theory of equations

Question

The condition for the roots of the equation,
$(c^{2} - ab) x^{2} - 2 (a^{2} - bc) x + (b^{2} - ac) = 0$ to be equals

Moderate

A

$a = 0$
B

$b = 0$
C

$c = 0$
D

None of these

Solution

According to question,
$4 {(a^{2} - bc)}^{2} - 4 (c^{2} - ab) (b^{2} - ac) = 0$
$\Rightarrow a (a^{3} + b^{3} + c^{3} - 3 abc) = 0$
$\Rightarrow a = 0 or a^{3} + b^{3} + c^{3} = 3 abc$

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