Final answer:
The solutions to the quadratic equation 4x² + 3x - 1 = 0 are found using the quadratic formula, yielding two real solutions: x = 0.25 and x = -1.
Step-by-step explanation:
To find the solutions to the quadratic equation 4x² + 3x - 1 = 0, we can use the quadratic formula. The quadratic formula is √x = −b ± √(b² - 4ac) / (2a), where 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term. In this equation, a = 4, b = 3, and c = −1.
First, we calculate the discriminant (b² - 4ac), which is (3² - 4×4×(−1)) = 9 + 16 = 25. Since the discriminant is positive, we know there will be two real solutions.
Now, we apply the quadratic formula:
√x = −(3) ± √(25) / (2×4)
√x = −(3) ± 5 / 8
√x = (−3 + 5) / 8 or (−3 − 5) / 8
√x = 2 / 8 or −8 / 8
√x = 0.25 or − 1
Therefore, the two solutions to the equation are x = 0.25 and x = −1.