Discriminant of a quadratic equation
How many solutions does the equation $2x^2+2x+3=0$ have?
$D = 4 - 24 =-20 < 0$, discriminant negative, therefore we can affirm that the equation has no solution.
None
What must the value of $c$ be, so that the equation $x^2+4x+c=0$ has just one solution?
$D = 16 - 4c$, so, if we want just one solution, it must be $D = 0$, or $16 - 4c = 0$, and so, $c = \dfrac{16}{4} = 4$
$$4$$
Construct a quadratic equation whose discriminant is $30$.
This question has many possible answers. One of them might be $7x^2+4x-\dfrac{1}{2}=0$.
$$7x^2+4x-\dfrac{1}{2}=0$$