Math Question

Some of the steps in the derivation of the quadratic formula are shown.
Which best explains why the expression \( \pm \sqrt{b^{2}-4 a c} \) \( \operatorname{step} 4: \frac{-4 a c+b^{2}}{4 a}=a\left(x+\frac{b}{2 a}\right)^{2} \) cannot be rewritten as \( b \pm \sqrt{-4 \alpha} \) during the next step?
\( \operatorname{step} 5:\left(\frac{1}{a}\right) \frac{b^{2}-4 a c}{4 a}=\left(\frac{1}{a}\right) a\left(x+\frac{b}{2 a}\right)^{2} \)
Negative values, like \( -4 a c \), do not have a square root.

The \( \pm \) symbol prevents the square root from being evaluated.
Step \( 6: \frac{b^{2}-4 a c}{4 a^{2}}=\left(x+\frac{b}{2 a}\right)^{2} \)
The square root of terms separated by addition and subtraction cannot be calculated individually.
Step \( 7: \frac{\pm \sqrt{b^{2}-4 a c}}{2 a}=x+\frac{b}{2 a} \) The entire term \( b^{2}-4 a c \) must be divided by \( 2 a \) before its square root can be determined.



AIR MATH homework app,
absolutely FOR FREE!

  • AI solution in just 3 seconds!
  • Free live tutor Q&As, 24/7
  • Word problems are also welcome!

Scan the QR code below
to download AIR MATH!