Joyce is trying to solve the equation y = x2 − 8x + 7 using the quadratic formula. She has made an error in one of the steps below. Find the step where Joyce went wrong. Step 1: x equals negative 8 plus or minus the square root of the quantity eight squared minus four times one times seven, end q Step 2: x equals negative 8 plus or minus the square root of sixty-four minus twenty-eight all over two times one. Step 3: x equals negative 8 plus or minus the square root of thirty-six all over two times one. Step 4: x equals negative 8 plus or minus six all over two.

The error is in the first step. It should be (+8 plus or minus the square root of the quantity eight squared minus four times one times seven ). This is because "b" is -8 so -b is -(-8) = +8

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tutorconsortium005 tutorconsortium005 · Answer 2 · 2022-06-15T10:17:50+02:00

The error is in the first step itself. She wrote -8 only instead of writing -(-8) in the quadratic formula. The quadratic formula is used for finding the roots of the quadratic equation.

What is the quadratic formula?

To solve a quadratic equation and find its roots we apply one of the methods of solving. That is the quadratic formula.

The quadratic formula is:

x = [-b ± √b² - 4ac]/2a

where the standard form of the quadratic equation is ax² + bx +c = 0

Solving the given quadratic equation:

The given equation is y = x²- 8x + 7

In comparing with the standard form of the quadratic equation we get

a = 1, b = -8 and c = 7

Applying the quadratic formula in a stepwise manner:

x = [-b ± √b² - 4ac]/2a

Step 1:

x = [-(-8) ± √(-8)² - 4×1×7]/2×1

Step 2:

x = [8 ± √64 - 28]/2×1

Step 3:

x = [8 ± √36]/2×1

Step 4:

x = [8 ± 6]/2

So, the steps are as shown above. From this, we can say that Joyce made an error in step 1 by writing only -8 instead of writing -(-8) since we have b = -8.

Learn more about quadratic formula here:

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