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Chapter 0: Problem 79

Solve each quadratic equation using the quadratic formula. $$3 x^{2}-3 x-4=0$$

Short Answer

Expert verified
The solutions to the quadratic equation \(3x^2 - 3x - 4 = 0\) are \(x = (3 + \sqrt{57}) / 6\) and \(x = (3 - \sqrt{57}) / 6\).

Step by step solution

01

Identify the coefficients

First identify the coefficients a, b, and c from the quadratic equation \(3x^2 - 3x - 4 = 0\). In this case, a=3, b=-3, and c=-4.
02

Calculate the Discriminant

Next, calculate the discriminant, which is the expression \(b^2 - 4ac\). Substituting the values of a, b, and c, we find that the discriminant is \((-3)^2 - 4*(3)(-4) = 9 + 48 = 57\).
03

Use the quadratic formula to find the roots

Now, use the quadratic formula to calculate the roots (solutions) of the quadratic equation. This gives us \(x = [-(-3) 卤 \sqrt{57}] / 2*3\), which simplifies to \(x = (3 卤 \sqrt{57}) / 6\).

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