Answer: C) Taking the square root of both .
Step-by-step explanation: We are given the two of the steps in the derivation of the quadratic formula:
Step 6: => [tex]\frac{b^2-4ac}{4a^2} = (x+\frac{b}{2a})^2[/tex]
Step 7: => [tex]\sqrt\frac{b^2-4ac}{4a^2}}= x+\frac{b}{2a})[/tex]
We can see in step, we have square on right side on ( x+b/2a ).
So, we need to get rid square by taking square root on both sides.
Square root of ( x+b/2a )^2 is just x+b/2a.
And we got [tex]\sqrt\frac{b^2-4ac}{4a^2}} [/tex] on left side.
Also if we simplify denominator [tex]\sqrt{4a^2}[/tex], we get 2a.
So, final expression for step 7 is
Step 7: => [tex]\frac{\sqrt{b^2-4ac}}{2a}}=x+\frac{b}{2a}[/tex].
Therefore, they performed operation: C) Taking the square root of both .
The operation that is performed in the derivation of the quadratic formula moving from Step 6 to Step 7 is taking the square root of both sides of the equation.
A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
Given that the step6 is:
[tex]\dfrac{b^2-4ac}{4a^2}= (\dfrac{x+b}{2a})^2[/tex]
while the step7 is:
[tex]\sqrt{\dfrac{b^2-4ac}{4a^2}}= (\dfrac{x+b}{2a})[/tex]
The operation that is performed in the derivation of the quadratic formula moving from Step 6 to Step 7 is taking the square root of both sides of the equation.
Learn more about Quadratic Equations:
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