QuestionAugust 26, 2025

34 Using the quadratic formula, solve x^2-6x+3=0 Express the answer in simplest radical form.

34 Using the quadratic formula, solve x^2-6x+3=0 Express the answer in simplest radical form.
34 Using the quadratic formula, solve x^2-6x+3=0 Express the answer in simplest radical form.

Solution
4.3(337 votes)

Answer

x = 3 + \sqrt{6}, \; x = 3 - \sqrt{6} Explanation 1. Identify coefficients Coefficients are a = 1, b = -6, c = 3. 2. Apply the quadratic formula Use **x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}**. Substitute a, b, and c: x = \frac{-(-6) \pm \sqrt{(-6)^2 - 4 \cdot 1 \cdot 3}}{2 \cdot 1}. 3. Calculate discriminant Discriminant is b^2 - 4ac = (-6)^2 - 4 \cdot 1 \cdot 3 = 36 - 12 = 24. 4. Simplify square root \sqrt{24} = \sqrt{4 \times 6} = 2\sqrt{6}. 5. Solve for x x = \frac{6 \pm 2\sqrt{6}}{2}. Simplify: x = 3 \pm \sqrt{6}.

Explanation

1. Identify coefficients<br /> Coefficients are $a = 1$, $b = -6$, $c = 3$.<br />2. Apply the quadratic formula<br /> Use **$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$**. Substitute $a$, $b$, and $c$: $x = \frac{-(-6) \pm \sqrt{(-6)^2 - 4 \cdot 1 \cdot 3}}{2 \cdot 1}$.<br />3. Calculate discriminant<br /> Discriminant is $b^2 - 4ac = (-6)^2 - 4 \cdot 1 \cdot 3 = 36 - 12 = 24$.<br />4. Simplify square root<br /> $\sqrt{24} = \sqrt{4 \times 6} = 2\sqrt{6}$.<br />5. Solve for x<br /> $x = \frac{6 \pm 2\sqrt{6}}{2}$. Simplify: $x = 3 \pm \sqrt{6}$.
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