First slide

Theory of equations

Question

If a is real number, then minimum number of real roots of equation $(x^{2} + a x + 1) (3 x^{2} + a x - 3) = 0$ can be

Moderate

Solution

$\begin{array}{l} D_{1} = a^{2} - 4 \\ D_{2} = a^{2} + 36 > 0 \end{array} n o w D_{1} + D_{2} = 2 a^{2} + 32 > 0$
So, the equation has at least two real roots.

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