Question: Which of the following is the correct solution to the quadratic equation 4x ^ 2 – 5x – 12 = 0?
- x = 5/8 + i√167/8
- x = 5/8 – i√167/8
- x = -3/8 + i√167/8
- x = -3/8 – i√167/8
Answer: A) x = 5/8 + i√167/8
4x ^ 2 – 5x – 12 = 0 Solution:
We can solve the quadratic equation 4x^2 - 5x - 12 = 0 Using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation.
In this case, a = 4, b = -5, and c = -12. The formula is given by x = (-b ± √(b² – 4ac)) / 2a. Plugging in the values, the discriminant becomes (-5)² – 4(4)(-12) = 25 + 192 = 217. Since the discriminant is positive, the equation has two real and distinct solutions. After simplifying further, you can find the exact values for x. The quadratic equation 4x² – 5x – 12 = 0 is a classic example of solving equations with the quadratic formula.
In this case, a = 4, b = -5, and c = -12. Substituting these values into the quadratic formula, we get:
x = (-(-5) ± √((-5)² - 4 * 4 * -12)) / 2 * 4
x = (5 ± √(225 + 192)) / 8
x = (5 ± √417) / 8
x = 5/8 ± i√167/8
Therefore, the correct solution to the quadratic equation 4x^2 - 5x - 12 = 0 is x = 5/8 + i√167/8.
Solve the equation (2x+2)/4 = (x-3)/3
To solve the equation (2x + 2)/4 = (x – 3)/3, begin by eliminating the fractions. Multiply both sides by 12, the least common multiple of 4 and 3. This gives you:
3(2x + 2) = 4(x – 3).
Now, distribute on both sides:
6x + 6 = 4x – 12.
Next, subtract 4x from both sides:
2x + 6 = -12.
Now, subtract 6 from both sides:
2x = -18.
Finally, divide by 2:
x = -9.
Thus, the solution to (2x + 2)/4 = (x – 3)/3 is x = -9.
