Question

If the solutions to an equation are 2 and –3, which of the following could be the equation?

A. x^2-x-6=0
B. 3x – 6 = 0
C. 3x^2-15x+18=0
D. 2x^2+2x=12

Answer 1

The solutions are 2 and -3 so we can write our equation as:


`a\cdot(x-2)(x+3)=0\\\\a\cdot(x^2-2x+3x-6)=0\\\\a\cdot(x^2+x-6)=0\\\\ax^2+ax-a\cdot6=0`

and for a = 2 there will be:


`ax^2+ax-a\cdot6=0\\\\ 2x^2+2x-2\cdot6=0\\\\ 2x^2+2x-12=0\quad|+12\\\\\boxed{2x^2+2x=12}`

Answer D.