Question

Some of the steps in the derivation of the quadratic formula are shown.

Step 4: StartFraction negative 4 a c + b squared Over 4 a EndFraction = a ( x + StartFraction b Over 2 a EndFraction) squared

Step 5: (StartFraction 1 Over a EndFraction) StartFraction b squared minus 4 a c Over 4 a EndFraction = (StartFraction 1 Over a EndFraction) a (x + StartFraction b Over 2 a EndFraction) squared

Step 6: StartFraction b squared minus 4 a c Over 4 a squared EndFraction = ( x + StartFraction b Over 2 a EndFraction) squared

Step 7: StartFraction plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction = x + StartFraction b Over 2 a EndFraction
Which best explains why the expression plus or minus StartRoot b squared minus 4 a c EndRoot cannot be rewritten as b plus or minus StartRoot negative 4 a c EndRoot during the next step?

Negative values, like −4ac, do not have a square root.
The ± symbol prevents the square root from being evaluated.
The square root of terms separated by addition and subtraction cannot be calculated individually.
The entire term b2 − 4ac must be divided by 2a before its square root can be determined.

Answer 1

C

Explanation:

Took the test on edge.

Answer 2

(C)The square root of terms separated by addition and subtraction cannot be calculated individually.

Explanation:

In Step 7:

`(\pm√(b^2-4ac) )/(2a) =x+(b )/(2a)`

The expression
`\pm√(b^2-4ac)` cannot be written as
`b \pm√(4ac)`. This is as a result of the fact that square roots of terms separated by addition and subtraction cannot be calculated individually.

Take these examples:

`√(9-4) =√(5) \\√(9)-√(4)=3-2=1\\ $Clearly √(5)\\eq 1\\$Similarly\\√(9+4) =√(13) \\√(9)+√(4)=3+2=5\\ $Clearly √(13)\\eq 5\\`