For the quadratic equation 5x^2 + 3x - 2 = 0, what is the value of the roots usi

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Question: For the quadratic equation 5x^2 + 3x - 2 = 0, what is the value of the roots using the quadratic formula? (2023)

Options:

Correct Answer: -1, 2/5

Exam Year: 2023

Solution:

Using the quadratic formula x = [-b ± √(b^2 - 4ac)] / 2a, we find the roots to be -1 and 2/5.

For the quadratic equation 5x^2 + 3x - 2 = 0, what is the value of the roots using the quadratic formula? (2023)

For the quadratic equation 5x^2 + 3x - 2 = 0, what is the value of the roots using the quadratic formula? (2023)

Step 1: Identify the coefficients a, b, and c from the quadratic equation 5x^2 + 3x - 2 = 0. Here, a = 5, b = 3, and c = -2.
Step 2: Write down the quadratic formula: x = [-b ± √(b^2 - 4ac)] / 2a.
Step 3: Calculate b^2 - 4ac. First, find b^2: 3^2 = 9. Then calculate 4ac: 4 * 5 * -2 = -40. Now, compute b^2 - 4ac: 9 - (-40) = 9 + 40 = 49.
Step 4: Take the square root of 49, which is 7.
Step 5: Substitute the values into the quadratic formula. We have x = [-3 ± 7] / (2 * 5).
Step 6: Calculate the two possible values for x. First, for the plus sign: x = (-3 + 7) / 10 = 4 / 10 = 2/5. Second, for the minus sign: x = (-3 - 7) / 10 = -10 / 10 = -1.
Step 7: The roots of the equation are x = -1 and x = 2/5.

Quadratic Formula – The quadratic formula is used to find the roots of a quadratic equation in the form ax^2 + bx + c = 0.
Discriminant – The discriminant (b^2 - 4ac) determines the nature of the roots (real and distinct, real and equal, or complex).
Coefficient Identification – Identifying the coefficients a, b, and c from the quadratic equation is crucial for applying the formula correctly.