Question

Use the quadratic formula to solve the equation. $$2 x^{2}+4 x-3=0$$

Short answer

The roots of the equation are \(x = -1 + \sqrt{10}\) and \(x = -1 - \sqrt{10}\).

Step-by-step solution

Identify the coefficients

The equation \(2x^2 + 4x - 3 = 0\) is a quadratic equation. The coefficients are \(a = 2\), \(b = 4\), and \(c = -3\).

Compute the discriminant

For the quadratic formula, we need to calculate the value of the discriminant, which is \(b^2 - 4ac\). By substituting our values into the equation, we get \(16 - 4*2*(-3) = 16 + 24 = 40\)

Find the roots using the quadratic formula

The roots of the equation can be found using the quadratic formula \(-b \pm \sqrt{b^2 - 4ac} \over 2a\). Substituting the earlier computed values into this formula, we get the roots of the equation as \(x = -4 \pm \sqrt{40} \over 4\). This simplifies to \(x = -1 \pm \sqrt{10}\)