Question

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Part 1
Determine whether the following statement is true of false. If the statement is​ false, make the necessary​ change(s) to produce a true statement.
In using the quadratic formula to solve the quadratic equation 4 x squared equals 7 x minus 5​, we have aequals4​, bequals7​, and cequalsminus5.
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Part 1
Choose the correct answer below.
A.
The statement is true.
B.
The statement is false. When using the quadratic formula to solve 4 x squared equals 7 x minus 5​, we should have aequals4​, bequals7​, and cequals5.
C.
The statement is false. When using the quadratic formula to solve 4 x squared equals 7 x minus 5​, we should have aequals4​, bequalsminus7​, and cequalsminus5.
D.
The statement is false. When using the quadratic formula to solve 4 x squared equals 7 x minus 5​, we should have aequals4​, bequalsminus7​, and cequals5.

Answer 1

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 \(ax^2 + bx + c = 0\).

1. Start with the original equation:
\[
4x^2 = 7x - 5
\]

2. 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 \(c = 5\).