Difference Between x^2 + ax + b and ax^2 + bx + c?

Thread starter Amaz1ng
Start date Apr 27, 2011
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Factoring

In summary, the expressions x^2 + ax + b and ax^2 + bx + c differ in the order of their terms. They can both be simplified and factored, with coefficients of x^2, x, and the constant term a, b, and c respectively. These expressions are related to the quadratic formula and the number of real solutions they have depends on the values of their coefficients.

Apr 27, 2011

Amaz1ng

Is there a difference between the form x^2 + ax + b and ax^2 + bx + c? I ask because I can use the AC factoring method for them both.

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Apr 27, 2011

chaoseverlasting

The AC factoring method? I don't know of that one. The first form is the same as the second form where a=1.

Apr 27, 2011

eczeno

they are the same. any quadratic expression in x can be expressed both ways.

cheers

FAQ: Difference Between x^2 + ax + b and ax^2 + bx + c?

What is the difference between x^2 + ax + b and ax^2 + bx + c?

The main difference between these two expressions is the order of the terms. In x^2 + ax + b, the highest degree term is x^2, followed by ax and then a constant term b. In ax^2 + bx + c, the highest degree term is ax^2, followed by bx and then a constant term c.

Can these expressions be simplified or factored?

Yes, both expressions can be simplified and factored. In x^2 + ax + b, we can factor out an x to get x(x + a) + b. In ax^2 + bx + c, we can factor out an a to get a(x^2 + bx/a + c/a).

What are the coefficients of x^2, x, and the constant term in each expression?

In x^2 + ax + b, the coefficient of x^2 is 1, the coefficient of x is a, and the constant term is b. In ax^2 + bx + c, the coefficient of x^2 is a, the coefficient of x is b, and the constant term is c.

How do these expressions relate to the quadratic formula?

Both expressions are quadratic equations, which are typically solved using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. The values of a, b, and c in the expressions correspond to the coefficients in the formula.

Are there any real solutions for these expressions?

The solutions of these expressions depend on the values of a, b, and c. If the discriminant (b^2 - 4ac) is positive, there will be two real solutions. If the discriminant is zero, there will be one real solution. If the discriminant is negative, there will be no real solutions.