Multiple Choice
Solve the given quadratic equation using the quadratic formula.
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1. Equations and Inequalities
The Quadratic Formula
Multiple Choice
Solve the given quadratic equation using the quadratic formula.
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Verified step by step guidance1
First, rewrite the quadratic equation in standard form: \(2x^2 - 3x + 3 = 0\).
Identify the coefficients \(a\), \(b\), and \(c\) from the equation \(ax^2 + bx + c = 0\). Here, \(a = 2\), \(b = -3\), and \(c = 3\).
Apply the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\). Substitute the values of \(a\), \(b\), and \(c\) into the formula.
Calculate the discriminant \(b^2 - 4ac\). If the discriminant is negative, the solutions will involve imaginary numbers.
Simplify the expression \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\) to find the two possible values for \(x\).
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