Question
Completing the Square & the Quadratic Formula Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
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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
Answers
GPT-4o mini
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.
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.