Is expansion necessary for this quadratic equation?

In summary, the given expression cannot be simplified into a quadratic equation without multiplying the expressions under the brackets. Expanding the expression is necessary to solve for x.
  • #1
Kartik.
55
1
(x+3)(x-4)(x-2)(x+1) = 24
Can we change it into a quadratic equation without multiplying the expressions under those brackets?
 
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  • #2
Kartik. said:
(x+3)(x-4)(x-2)(x+1) = 24
Can we change it into a quadratic equation without multiplying the expressions under those brackets?

No, this will be a quartic (4th degree in x) whichever way you play with it. You can easily see this because the only way for it to become a quadratic is if the LHS x4 and x3 coefficients are cancelled, which isn't going to happen since the RHS only has a constant.
 
  • #3
Kartik. said:
(x+3)(x-4)(x-2)(x+1) = 24
Can we change it into a quadratic equation without multiplying the expressions under those brackets?

You should realize that 3 times 4 times 2 is equal to 24, so you definitely want to expand.
 

1. What is a quadratic equation?

A quadratic equation is a mathematical expression in the form of ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. It is a second-degree polynomial equation and can have up to two solutions.

2. What is the purpose of a quadratic equation?

A quadratic equation is used to solve problems involving quadratic relationships, such as finding the maximum or minimum value of a quadratic function, determining the roots of a quadratic equation, and solving real-world problems related to motion, area, and volume.

3. How do you solve a quadratic equation?

There are several methods to solve a quadratic equation, including factoring, using the quadratic formula, completing the square, and graphing. The most commonly used method is the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / 2a.

4. Can a quadratic equation have more than two solutions?

No, a quadratic equation can have a maximum of two solutions. This is because a quadratic equation is a second-degree polynomial, meaning it can only have a maximum of two roots. However, it is possible for a quadratic equation to have less than two solutions, or no real solutions at all.

5. How are quadratic equations used in real life?

Quadratic equations are used in various fields, such as physics, engineering, and economics, to model and solve real-world problems. For example, they can be used to calculate the trajectory of a projectile, determine the optimal dimensions of a structure, or analyze the profit and loss of a business. They are also used in computer graphics to create curves and shapes.

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