Completing the Square & the Quadratic Formula Practice

Question

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Question
How many real solutions does the following quadratic equation have?

25x2+60x+36=0

(1 point)
solution(s)
Remaining Attempts : 3

Answer 1

To determine how many real solutions the quadratic equation \(25x^2 + 60x + 36 = 0\) has, we can use the discriminant of the quadratic formula.

The discriminant \(\Delta\) is given by the formula: \[ \Delta = b^2 - 4ac \] where \(a\), \(b\), and \(c\) are the coefficients from the quadratic equation \(ax^2 + bx + c = 0\).

For the given equation:

• \(a = 25\)
• \(b = 60\)
• \(c = 36\)

Now, we calculate the discriminant: \[ \Delta = 60^2 - 4 \cdot 25 \cdot 36 \] \[ \Delta = 3600 - 3600 \] \[ \Delta = 0 \]

The discriminant is \(0\), which indicates that there is exactly one real solution (a repeated root) for the quadratic equation.

So, the answer is: 1 solution.