Question

find the discriminant of the quadratic equation. determine the number of real solutions.
$5x^2 + 10x + 5 = 0$
what is the discriminant of the quadratic equation?
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Explanation:

Step1: Recall discriminant formula

For a quadratic equation \(ax^{2}+bx + c = 0\), the discriminant \(D\) is given by \(D=b^{2}-4ac\).

Step2: Identify \(a\), \(b\), \(c\)

In the equation \(5x^{2}+10x + 5 = 0\), we have \(a = 5\), \(b = 10\), \(c = 5\).

Step3: Calculate discriminant

Substitute the values into the formula: \(D=(10)^{2}-4\times5\times5\)
\(= 100 - 100\)
\(= 0\)

Answer:

The discriminant of the quadratic equation \(5x^{2}+10x + 5 = 0\) is \(0\). And since the discriminant is \(0\), the quadratic equation has exactly one real solution.