Respuesta :
The equation that is true for x = -6 and x= 2 is given by: Option B: 2x^2 +8x -24 = 0
What are those values of the variables called for which an equation is true?
Suppose there is an equation given, involving some variables.
Then, those values of the involved variable, for which the equation is true, are called solution of the equation.
For single variable equations, specially for polynomials, these solutions are called the roots of the equation.
How to find the roots of a quadratic equation?
Suppose that the given quadratic equation is
[tex]ax^2 + bx + c = 0[/tex]
Then its roots are given as:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
For this case, the options are all quadratic equations, so we can check all the options to find the roots to see if they match to x = -6 and = 2
- Option 1: [tex]2x^2 -16x + 12 = 0[/tex]
Then its roots are given as:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \dfrac{-(-16) \pm \sqrt{(-16)^2 - 4(2)(12)}}{2(2)}\\\\x = \dfrac{16 \pm \sqrt{196 - 96}}{4} = \dfrac{16 \pm 10}{4}\\\\x = 26/4, x = 6/4[/tex]
Thus, this equation isn't true for both x = -6 and x= 2
- Option 2: [tex]2x^2 +8x -24 = 0[/tex]
Then its roots are given as:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \dfrac{-8 \pm \sqrt{(8)^2 - 4(2)(-24)}}{2(2)}\\\\x = \dfrac{-8 \pm \sqrt{64 +192}}{4} = \dfrac{-8 \pm 16}{4}\\\\x = -6, x = 2[/tex]
Thus, this equation is true for both x = -6 and x= 2
Since the question says "Which equation is true", so that means only one option is true.
Thus, the equation that is true for x = -6 and x= 2 is given by: Option B: [tex]2x^2 +8x -24 = 0[/tex]
Learn more about finding the solutions of a quadratic equation here:
https://brainly.com/question/3358603
