Roots of the quadratic equation

Find the roots of the quadratic equation 3𝑥^2 4𝑥 + 1 = 0

Sample Answer

To find the roots of the quadratic equation (3x^2 + 4x + 1 = 0), we can use the quadratic formula:

The quadratic formula is given by: (x = frac{-b pm sqrt{b^2 – 4ac}}{2a})

In this equation, (a = 3), (b = 4), and (c = 1). Plugging these values into the formula:

(x = frac{-4 pm sqrt{4^2 – 431}}{2*3})

(x = frac{-4 pm sqrt{16 – 12}}{6})

(x = frac{-4 pm sqrt{4}}{6})

(x = frac{-4 pm 2}{6})

Now, we have two possible solutions for x:

1. When using the plus sign: (x_1 = frac{-4 + 2}{6} = frac{-2}{6} = -frac{1}{3})

2. When using the minus sign: (x_2 = frac{-4 – 2}{6} = frac{-6}{6} = -1)

Therefore, the roots of the quadratic equation (3x^2 + 4x + 1 = 0) are (x = -frac{1}{3}) and (x = -1).

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