Find and explain the error in the student’s work below.
Solve 2x² - 5x -12 = 0 using the Quadratic Formula.
The student's work is not provided, so we cannot find and explain the error. Please provide the student's work for further assistance.
To find the error, let's first understand how to solve the quadratic equation using the Quadratic Formula.
The Quadratic Formula is: x = (-b ± √(b^2 - 4ac)) / (2a)
Now, let's analyze the student's work:
Solve 2x² - 5x - 12 = 0 using the Quadratic Formula.
1. Find the values of a, b, and c:
- a = 2
- b = -5
- c = -12
2. Apply the values to the Quadratic Formula:
x = (-(-5) ± √((-5)^2 - 4(2)(-12))) / (2(2))
3. Simplify:
x = (5 ± √(25 + 96)) / 4
x = (5 ± √(121)) / 4
4. Calculate the square root of 121:
√(121) = 11
5. Substitute the value back into the equation:
x = (5 ± 11) / 4
At this point, we found the error in the student's work. The error lies in the calculation of the discriminant, which should be (b^2 - 4ac).
In this case:
Discriminant = (-5)^2 - 4(2)(-12)
= 25 + 96
= 121
The discriminant is 121, not (25 + 96) which the student mistakenly calculated.
Let's correct the calculation:
x = (5 ± √(121)) / 4
Since √(121) = 11, we have:
x = (5 ± 11) / 4
Now, we can continue solving for x.
The quadratic equation that needs to be solved is:
2x² - 5x - 12 = 0
To solve this equation using the quadratic formula, we first need to determine the values of a, b, and c in the quadratic equation of the form ax² + bx + c = 0.
In this equation, a = 2, b = -5, and c = -12.
Now, let's substitute these values into the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Plugging in the values:
x = (-(-5) ± √((-5)² - 4(2)(-12))) / (2(2))
Simplifying:
x = (5 ± √(25 + 96)) / 4
x = (5 ± √121) / 4
x = (5 ± 11) / 4
This leads to two potential solutions:
x₁ = (5 + 11) / 4 = 16 / 4 = 4
x₂ = (5 - 11) / 4 = -6 / 4 = -3/2
Therefore, the solutions to the equation 2x² - 5x - 12 = 0 are x = 4 and x = -3/2.
To identify the error in the student's work, we would need to see their solution and compare it to the correct solution.