Two of the steps in the derivation of the quadratic formula are shown below. 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 1 a EndFraction = x + StartFraction b Over 2 a EndFraction Which operation is performed in the derivation of the quadratic formula moving from Step 6 to Step 7? subtracting StartFraction b Over 2 a EndFraction from both sides of the equation squaring both sides of the equation taking the square root of both sides of the equation taking the square root of the discriminant
2 answers:
Explanation:
Step-by-step clarification:
Referring to step 6
(b² — 4ac) / 4a² = (x + b/2a)²
The mistake in the question is that it should be (x + b/2a)²
According to step 7
±√(b² —4ac) /2a = x + b/2a
The error in the question is that it should be divided by 2a, not 1a.
1. The transition from step 6 to step 7 involves taking the square roots of both sides
(b² — 4ac) / 4a² = (x + b/2a)²
Taking the square of both sides
√(b²—4ac) / √4a² = √(x + b/2a)²
√(b²—4ac) / 2a = x + b/2a
This forms step 7 correctly.
Next, subtracting b/2a from both sides
√(b²—4ac) / 2a - b/2a= x + b/2a -b/2a
√(b²—4ac) / 2a — b/2a = x
(√(b²—4ac) — b)/2a = x
x = [—b ± √(b²—4ac)] / 2a
This gives the desired formula.
The discriminant is D = b²—4ac.
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