Question

Solve for x: 3x^2 + 7x - 4 = 0

a) x = -4, x = 1/3
b) x = -1, x = 4/3
c) x = -3, x = 4/3
d) x = -1, x = 3/2

Factor: 36 - 49^2y

a) 7(7y - 6)(7y + 6)
b) 5(5y - 6)(5y + 6)
c) 13(13y - 6)(13y + 6)
d) 12(12y - 6)(12y + 6)

Solve for v: v^2 - 7v + 6 = 0

a) v = 1, v = 6
b) v = 2, v = 5
c) v = 3, v = 4
d) v = 6, v = 1

Answer 1

1. For the quadratic equation 3x² + 7x - 4 = 0, the correct solution is (b) x = -1, x = 4/3.

2. The factorization of 36 - 49²y is (a) 7(7y - 6)(7y + 6).

3. Solving the quadratic equation v² - 7v + 6 = 0 yields (c) v = 3, v = 4.

Step-by-step explanation:

1. In solving the quadratic equation 3x² + 7x - 4 = 0, we can use the quadratic formula, which is given by x = [-b ± √(b² - 4ac)] / 2a. Here, a = 3, b = 7, and c = -4. Substituting these values into the formula and simplifying, we find the solutions to be x = -1 and x = 4/3. Thus, the correct answer is (b) x = -1, x = 4/3.

2. To factorize 36 - 49²y, we recognize it as a difference of squares, where a² - b² = (a + b)(a - b). Here, a = 49y and b = 6. Applying the formula, we get (7y + 6)(7y - 6). Further simplification gives the correct factorization as (a) 7(7y - 6)(7y + 6).

3. For the quadratic equation v² - 7v + 6 = 0, we again use the quadratic formula with a = 1, b = -7, and c = 6. Substituting these values, we find v = 3 and v = 4. Thus, the correct solution is (c) v = 3, v = 4.