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

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

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

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

$4$

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How many solutions does the equation $2 x^{2} + 2 x + 3 = 0$ 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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