Use the quadratic formula to solve the equation. –4x2 – 3x + 2 = 0 (1 point) Responses Image with alt text: -3/8 plus or minus square root 41/8 Image with alt text: -8/3 plus or minus square root 82/8 Image with alt text: -3/8 plus or minus square root 20/2
The correct response is the first one: -3/8 plus or minus square root 41/8.
To solve the equation -4x^2 - 3x + 2 = 0 using the quadratic formula, we need to find the values of x that satisfy this equation.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Comparing the given equation to the standard quadratic equation (ax^2 + bx + c = 0), we can see that a = -4, b = -3, and c = 2.
Plugging these values into the quadratic formula, we have:
x = (-(-3) ± √((-3)^2 - 4(-4)(2))) / (2(-4))
Simplifying further:
x = (3 ± √(9 + 32)) / (-8)
x = (3 ± √(41)) / (-8)
Hence, the solutions to the equation -4x^2 - 3x + 2 = 0 are:
x = (-3 ± √41) / 8
To solve the quadratic equation -4x^2 - 3x + 2 = 0 using the quadratic formula, we can follow these steps:
1. Identify the coefficients:
- The coefficient of the x^2 term is -4.
- The coefficient of the x term is -3.
- The constant term is 2.
2. Substitute the coefficients into the quadratic formula:
The quadratic formula is: x = (-b ± √(b^2 - 4ac)) / 2a
Substituting the values from the given equation, we get:
x = (-(−3) ± √((−3)^2 - 4*(-4)*2)) / (2*(-4))
3. Simplify the equation inside the square root:
x = (-(-3) ± √(9 + 32)) / (-8)
x = (3 ± √41) / (-8)
4. Simplify further if necessary:
The simplified solutions are:
x = (-3 ± √41) / 8
So, the correct answer is: Image with alt text: -3/8 plus or minus square root 41/8.