Carrotsticks
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Since this section is a bit quiet at the moment, here's something to promote a bit of discussion.
=ax^2+bx+c $ (assume that a,b and c are real) is given by $ b^2-4ac. \\\\ $So for a quadratic to have no real roots, we must have $ b^2 - 4ac < 0. \\\\ $ Alternatively, we could let the roots be $ \alpha $ and $ \beta $ and analyse $ \alpha ^2 + \beta ^2. $ If we see that $ \alpha ^2 + \beta^2 < 0 $ then that means that both roots are complex. However, $ \alpha ^2 + \beta ^2 = \frac{b^2 - 2ac}{a^2} $ and if this is less than zero, we acquire $ b^2 - 2ac < 0 $ instead of our discriminant $ b^2 - 4ac < 0. \\\\ $Discuss why this is the case.$ )
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Something to ponder. (1 Viewer)
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Carrotsticks
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I actually intended for students to discuss this (concept of "sufficient + necessary condition" or "iff"), but thanks for answering anyway lol.
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RealiseNothing
what is that?It is Cowpea
It doesn't work both ways.
If
then both roots are complex.
But if both roots are complex, then is not necessarily true.
If
But if both roots are complex, then
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