Question

Layla needs to solve the quadratic equation x^2+x−6=4. Which statement about how Layla should solve this equation is true?

A: The quadratic formula is a good method because this quadratic equation cannot easily be factored
B: The quadratic formula is not a good method because you can factor the equation since -6 is divisible by 3
C: Layla cannot solve this quadratic equation because it is not set equal to 0
D: The quadratic formula is the only way to solve a quadratic equation

Answer 1

Choice A

Explanation:

Transposing 4 to the left side, the given equation is equivalent to

`x^2+x-6-4=0\\x^2+x-10=0.`

Statement A is correct since the given equation cannot be solved by factoring (i.e. there are no two numbers that have a product of -10 and a sum of 1, so it cannot be factored as (x+a)(x+b)=0.)

Statement B is incorrect since solving quadratic equations is not dependent on whether the constant (i.e. c=-6) is divisible by 3 or not.

Statement C is incorrect since the equation can be manipulated so that it is set equal to 0.

Statement D is incorrect since there are other methods of solving quadratic equations such as using completing the square method.