To fill in the blanks for the quadratic formula, we first need to understand the general form of a quadratic equation:
\[ ax^2 + bx + c = 0 \]
The corresponding values for the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Now we can fill in the blanks using the options provided (x, 1, 3, or 4):
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In the formula \( -b \), \( b \) can be either x, 1, 3, or 4. We’ll use the simplest option, which is:
- Fill in the first blank with: 1
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The expression under the square root \( b^2 - 4ac \) requires us to fill in:
- \( b = 1 \) fills in the second blank: \[1^2\]
- Choose \( a = 1 \) and \( c = 3 \) for this example.
- Fill in the third blank with: 3 (for \( c \))
- Fill in the fourth blank with: 1 (for \( a \))
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The denominator \( 2a \):
- Since we used \( a = 1 \),
- Fill in the last blank with: 1
Putting this together, your completed quadratic formula will be:
\[ -1 \pm \sqrt{1^2 - 4(1)(3)} \] \[ \frac{-1 \pm \sqrt{1}}{2(1)} \]
So the final filled-in version is:
\[ -1 \pm \sqrt{1^2 - 4 (1)(3)} \] \[ \frac{-1 \pm \sqrt{1}}{2(1)} \]
Keep in mind that there could be other combinations of values for \( a \), \( b \), and \( c \) depending on your specific needs or preferences!
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