Problems from Discriminant of a quadratic equation

Construct a quadratic equation whose discriminant is $$30$$.

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This question has many possible answers. One of them might be $$7x^2+4x-\dfrac{1}{2}=0$$.

$$7x^2+4x-\dfrac{1}{2}=0$$

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What must the value of $$c$$ be, so that the equation $$x^2+4x+c=0$$ has just one solution?

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$$D = 16 - 4c$$, so, if we want just one solution, it must be $$D = 0$$, or $$16 - 4c = 0$$, and so, $$c = \dfrac{16}{4} = 4$$

$$4$$

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How many solutions does the equation $$2x^2+2x+3=0$$ have?

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$$D = 4 - 24 =-20 < 0$$, discriminant negative, therefore we can affirm that the equation has no solution.

None

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