To determine whether the statement is true or false, we first need to rearrange the equation \(4x^2 = 7x - 5\) into standard form, which is \(ax^2 + bx + c = 0\).
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Start with the original equation: \[ 4x^2 = 7x - 5 \]
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Rearranging it to standard form (setting one side to zero): \[ 4x^2 - 7x + 5 = 0 \]
From this equation, we can identify the coefficients:
- \(a = 4\)
- \(b = -7\)
- \(c = 5\)
Now, let's evaluate the original statement: "we have \(a = 4\), \(b = 7\), and \(c = -5\)".
We can see that:
- \(a = 4\) is correct.
- \(b = 7\) is incorrect; it should be \(b = -7\).
- \(c = -5\) is incorrect; it should be \(c = 5\).
Given this analysis, the correct option is:
C. The statement is false. When using the quadratic formula to solve \(4x^2 = 7x - 5\), we should have \(a = 4\), \(b = -7\), and \(c = 5\).