First slide

Theory of equations

Question

If the roots of the equation $a x^{2} - 4 x + a^{2} = 0$ are imaginary and the sum of the roots is equal to their product, then $a =$

Moderate

Solution

We have,
$\begin{array}{l} 16 - 4 a^{3} < 0 and \frac{4}{a} = a \\ \Rightarrow 4 - a^{3} < 0 and a^{2} = 4 \\ \Rightarrow a^{3} - 4 > 0 and a = \pm 2 \Rightarrow a = 2 \end{array}$

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