Find the discriminant of $x^2 + 3x + 4$.
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\begin{align*}b^2 - 4ac &= 3^2 - 4\times1\times4\\&= -7\end{align*}
Find the discriminant of $2t^2 - 6t + 1$.
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\begin{align*}b^2 - 4ac &= (-6)^2 - 4\times2\times1\\&= 28\end{align*}
Find the discriminant of $3x^2 + (m+n)x - 1$ in terms of $m$ and $n$.
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\begin{align*}b^2 - 4ac &= (m+n)^2 - 4\times3\times(-1)\\&= (m+n)^2 + 12\end{align*}
Find the discriminant of $5q^2 + q + \frac{1}{2}$.
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\begin{align*}b^2 - 4ac &= 1^2 - 4\times5\times\frac{1}{2}\\&= -9\end{align*}
Find the discriminant of $2x^2 - px - q$ in terms of $p$ and $q$.
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\begin{align*}b^2 - 4ac &= (-p)^2 - 4\times2\times(-q)\\&= p^2 + 8q\end{align*}
Find the discriminant of $\frac{y^2}{3} + 2y - 6$.
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\begin{align*}b^2 - 4ac &= 2^2 - 4\times\frac{1}{3}\times(-6)\\&= 12\end{align*}
If $2x^2 - 3x - 3 = 0$, find $x$. The discriminant is $33$.
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\[x = \frac{-b\pm\sqrt\Delta}{2a} = \frac{3\pm \sqrt{33}}{4}\]
If $q^2 + 5q + 1 = 0$, find $q$. The discriminant is $21$.
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\[q = \frac{-b\pm\sqrt\Delta}{2a} = \frac{-5\pm \sqrt{21}}{2}\]
If $x^2 - px +1 = 0$, find $x$ in terms of $p$. The discriminant is $p^2 - 4$.
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\[x = \frac{-b\pm\sqrt\Delta}{2a} = \frac{p\pm \sqrt{p^2 - 4}}{2}\]
If $2t^2 -7t +4 = 0$, find $t$. The discriminant is $17$.
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\[t = \frac{-b\pm\sqrt\Delta}{2a} = \frac{7\pm \sqrt{17}}{4}\]
If $\frac{x^2}{2} -x -3 = 0$, find $x$. The discriminant is $7$.
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\[x = \frac{-b\pm\sqrt\Delta}{2a} = 1\pm \sqrt{7}\]
If $5y^2 + 9y +3 = 0$, find $y$. The discriminant is $21$.
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\[y = \frac{-b\pm\sqrt\Delta}{2a} = \frac{-9\pm \sqrt{21}}{10}\]
