Solving Quadratic Equations: X^2 + 5X + 12 = 0

2x^2+5x12=0 Solve the equation for x Brainly.in from brainly.in

Introduction

Quadratic equations are a type of equation that involves a variable raised to the power of two. Solving these equations can be challenging, but with the right approach, it can be done easily. In this article, we will discuss how to solve the quadratic equation x^2 + 5x + 12 = 0.

The Quadratic Formula

The quadratic formula is a formula that can be used to solve any quadratic equation. It is given by: x = (-b ± sqrt(b^2 - 4ac)) / 2a Where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.

Identifying Coefficients

Before we can use the quadratic formula, we need to identify the coefficients in the equation x^2 + 5x + 12 = 0. In this equation, a = 1, b = 5, and c = 12.

Using the Quadratic Formula

Now that we have identified the coefficients, we can use the quadratic formula to solve the equation: x = (-5 ± sqrt(5^2 - 4(1)(12))) / 2(1) Simplifying this equation gives us: x = (-5 ± sqrt(25 - 48)) / 2 x = (-5 ± sqrt(-23)) / 2

Complex Solutions

At this point, we have a problem. The square root of a negative number is not a real number, so we cannot simplify this equation any further using real numbers. Instead, we need to use complex numbers. The square root of -23 can be written as i*sqrt(23), where i is the imaginary unit. Therefore, our solutions are: x = (-5 + i*sqrt(23)) / 2 x = (-5 - i*sqrt(23)) / 2

Final Answer

These are the final answers to the quadratic equation x^2 + 5x + 12 = 0. They are complex numbers, but they are the only solutions to this equation.

Conclusion

Solving quadratic equations can be challenging, but with the right approach, it can be done easily. In this article, we discussed how to solve the quadratic equation x^2 + 5x + 12 = 0 using the quadratic formula. We also saw that sometimes the solutions to quadratic equations are complex numbers.