1. Equations and Inequalities

The Quadratic Formula

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Multiple Choice

Solve the given quadratic equation using the quadratic formula. $2x^2-3x=-3$

$x=\frac34+\frac{i\sqrt{15}}{4},x=\frac34-\frac{i\sqrt{15}}{4}$

$x=\frac34+\frac{5i}{4},x=\frac34-\frac{5i}{4}$

$x=\frac{3+\sqrt{15}}{4},x=\frac{3-\sqrt{15}}{4}$

$x=3+i\sqrt{15},x=3-i\sqrt{15}$

Verified step by step guidance

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 $x$.

Master Solving Quadratic Equations Using The Quadratic Formula with a bite sized video explanation from Patrick

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Expert video explanations

Solve the given quadratic equation using the quadratic formula. 2x2−3x=−32x^2-3x=-32x2−3x=−3