Questions: frac-(-2) pm sqrt(-2)^2-4()(-3)2(-3)

Solution Steps

To solve the quadratic equation using the quadratic formula, we need to identify the coefficients \(a\), \(b\), and \(c\) from the standard form \(ax^2 + bx + c = 0\). In this case, the equation is not fully provided, but assuming it is of the form \((-3)x^2 + (-2)x + c = 0\), we can use the quadratic formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Substitute \(a = -3\), \(b = -2\), and \(c\) (which is not provided, so we assume it to be 0 for this example) into the formula to find the roots.

The quadratic equation is assumed to be in the form \(-3x^2 - 2x + c = 0\). Here, the coefficients are identified as:

• \(a = -3\)
• \(b = -2\)
• \(c = 0\) (assumed since it was not provided)

The discriminant \(\Delta\) is calculated using the formula: \[ \Delta = b^2 - 4ac \] Substituting the values, we get: \[ \Delta = (-2)^2 - 4(-3)(0) = 4 \]

The roots of the quadratic equation are given by the quadratic formula: \[ x = \frac{-b \pm \sqrt{\Delta}}{2a} \] Substituting the values of \(a\), \(b\), and \(\Delta\), we find: \[ x_1 = \frac{-(-2) + \sqrt{4}}{2(-3)} = \frac{2 + 2}{-6} = -0.6667 \] \[ x_2 = \frac{-(-2) - \sqrt{4}}{2(-3)} = \frac{2 - 2}{-6} = 0 \]

Final Answer