With the equation 4×2 – 5x – 12 = 0, you can see that the quadratic equation is a degree 2 polynomial. We can solve this problem in a number of different ways. Factoring is a way to break a problem down into its parts and find its roots. A different method is the quadratic formula, which can be used to solve any quadratic problem. We can find the numbers of x that make the equation true by using these methods. By solving quadratic equations, we can find key points on a graph or use quadratic relationships to solve problems in the real world.
How to Solve Quadratic Equations: A Start with 4x^2 – 5x – 12 = 0
Quadratic equations are very important in math and can be used in many other fields as well. For instance, 4×2 – 5x – 12 = 0 is an example, where x is an unknown number.
When a, b, and c are constants, the solution ax2 + bx + c = 0 takes on a general form. What are the factors for a, b, and c in this case? They are 4, 5, and 12.
The second-degree polynomial equation 4×2 – 5x – 12 = 0 says that the highest power of x is 2. To find the answers, or roots, to this equation, we need to find the values of x that make it true.
The quadratic formula, factoring, and completing the square are some ways to solve quadratic problems. These methods offer organised ways of doing things.
Looking into and understanding quadratic equations like 42 – 5x – 12 = 0 can teach us important lessons about algebra basics and give us problem-solving skills that are useful in many areas of maths and beyond.
Figure out the roots of 4x^2 – 5x – 12 = 0 by factoring the quadratic equation.
When you divide a quadratic equation into smaller parts, which is called “factoring,” you can find solutions to the problems. Let’s use this method to find the roots of the problem 4×2 – 5x – 12 = 0.
We need to find two binomial expressions that, when multiplied together, give us the original quadratic equation so we can factor it. When you add two numbers together that add up to -5 (the coefficient of x), you get -48. This is the product of the coefficients of x2 and the constant term.
By looking at the factors of -48 and trying out different combos, we find that -8 and 6 meet the needs. This means that the quadratic equation can be written as (4x + 6)(x – 8) = 0.
By setting each number to zero, we find two possible answers: 4x + 6 = 0 and x – 8 = 0. At x = -3/2 and x = 8, we solve these equations independently.
So, the quadratic equation 4×2 – 5x – 12 = 0 can be broken down into its parts: (4x + 6)(x – 8) = 0. This shows that the roots are x = -3/2 and x = 8. Here are the answers. We can learn more about how quadratic equations work by solving them.
The quadratic formula can be used to solve the equation 4x^2 – 5x – 12 = 0.
The quadratic formula is a useful tool that lets us get exact answers to any quadratic problem. Use this math problem to find the roots of 42 – 5x – 12 = 0.
For an equation like ax2 + bx + c = 0, the quadratic formula says that the answers for x can be found by using the formula x = (-b (b2 – 4ac)) / (2a).
What our equation says is that A = 4, B = 5, and C = 12. We can use these numbers as replacements in the quadratic formula to find the results for x.
We get the following answer from the math: x = (-(-5) ((-5)2 – 4 * 4 * -12)) / (2 * 4)
x = (5 ± √(25 + 192)) / 8 x = (5 ± √217) / 8
To solve the quadratic problem 4×2 – 5x – 12 = 0, we need to find (5 + 217) / 8 and (5 – 217) / 8.
Using the quadratic formula, we can exactly solve quadratic equations, which leads to correct answers. This formula gives us a methodical way to find the roots of any quadratic equation, which lets us study and understand how they work.
Looking at the Answers: Finding Out What the Roots of 4x^2 – 5x – 12 = 0 Are and Why They Matter
We used factoring and the quadratic formula to figure out how to solve the problem 4×2 – 5x – 12 = 0. Now, let’s look at what these roots are and how important they are. 4x ^ 2 – 5x – 12 = 0
The roots that were found are (5 + 217)/8 and (5 – 217)/8. By looking at the properties of the roots, we can figure out how the equation acts.
The first sign that they are real solutions is that the roots of the problem are real numbers. This means that the graph of the equation and the x-axis should meet at these points.
Second, the roots are not whole numbers or rational numbers; they are irrational numbers that include the square root of 217. This means that it might be hard to speak about the answers in simple number terms.
There are also two separate messages at the roots, one positive and one negative. As the equation says, this shows where the parabolic arc goes across the x-axis twice.
The answers to the equation 4×2 – 5x – 12 = 0 are looked at in order to learn more about the equation and how it can be shown graphically. By giving us information about the points where two quadratic functions meet, these roots help us figure out how quadratic functions work.
