Question
Solve the quadratic equation
-3x^2 + 5x - 7=0
Write one exact solution in each box. You can add or remove boxes. If there are no real solutions, remove all boxes
-3x^2 + 5x - 7=0
Write one exact solution in each box. You can add or remove boxes. If there are no real solutions, remove all boxes
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve the quadratic equation \(-3x^2 + 5x - 7 = 0\), we can use the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Here, \(a = -3\), \(b = 5\), and \(c = -7\).
First, calculate the discriminant \(b^2 - 4ac\):
\[
b^2 = 5^2 = 25
\]
\[
4ac = 4 \cdot (-3) \cdot (-7) = 12 \cdot 7 = 84
\]
\[
b^2 - 4ac = 25 - 84 = -59
\]
Since the discriminant is negative (\(-59\)), there are no real solutions.
Therefore, we remove all boxes.
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Here, \(a = -3\), \(b = 5\), and \(c = -7\).
First, calculate the discriminant \(b^2 - 4ac\):
\[
b^2 = 5^2 = 25
\]
\[
4ac = 4 \cdot (-3) \cdot (-7) = 12 \cdot 7 = 84
\]
\[
b^2 - 4ac = 25 - 84 = -59
\]
Since the discriminant is negative (\(-59\)), there are no real solutions.
Therefore, we remove all boxes.
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