Multiple Choice
For a quadratic equation in standard form , what expression gives the discriminant?
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1. Equations & Inequalities
The Quadratic Formula
Multiple Choice
Solve the given quadratic equation using the quadratic formula.
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Verified step by step guidance1
Identify the coefficients from the quadratic equation 3x^2 + 4x + 1 = 0. Here, a = 3, b = 4, and c = 1.
Recall the quadratic formula: x = \(\frac{-b \pm \sqrt{b^2 - 4ac}\)}{2a}. This formula is used to find the roots of any quadratic equation ax^2 + bx + c = 0.
Substitute the values of a, b, and c into the quadratic formula: x = \(\frac{-4 \pm \sqrt{4^2 - 4 \cdot 3 \cdot 1}\)}{2 \(\cdot\) 3}.
Calculate the discriminant, which is the expression under the square root: b^2 - 4ac = 16 - 12 = 4.
Simplify the expression: x = \(\frac{-4 \pm \sqrt{4}\)}{6}. Then, solve for the two possible values of x by considering both the positive and negative square roots.
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