Solving the Quadratic Expression: 3x^2 + 2x - 5
In this article, we will explore the solution to the quadratic expression 3x^2 + 2x - 5.
Understanding the Expression
The given expression is a quadratic expression, which means it has a degree of two. The general form of a quadratic expression is ax^2 + bx + c, where a, b, and c are constants. In this case, a = 3, b = 2, and c = -5.
Factoring the Expression
One way to solve a quadratic expression is to factor it, if possible. Factoring involves expressing the expression as a product of two binomials. However, in this case, the expression 3x^2 + 2x - 5 cannot be factored easily.
Using the Quadratic Formula
When a quadratic expression cannot be factored, we can use the quadratic formula to find its solutions. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, we have a = 3, b = 2, and c = -5. Plugging these values into the formula, we get:
x = (-(2) ± √((2)^2 - 4(3)(-5))) / 2(3) x = (-2 ± √(4 + 60)) / 6 x = (-2 ± √64) / 6 x = (-2 ± 8) / 6
Simplifying the Solutions
Now, we have two possible solutions:
x = (-2 + 8) / 6 = 6 / 6 = 1 x = (-2 - 8) / 6 = -10 / 6 = -5/3
Therefore, the solutions to the quadratic expression 3x^2 + 2x - 5 are x = 1 and x = -5/3.
Conclusion
In this article, we have solved the quadratic expression 3x^2 + 2x - 5 using the quadratic formula. We have found that the solutions to the expression are x = 1 and x = -5/3.
