Create a quadratic equation with the solutions x=-2 and x=6
would x=-2 = x=0
would x=6 = x = 0?
No, that is incorrect. When we say x=-2 and x=6 are the solutions, it means that when you substitute x=-2 or x=6 into the quadratic equation, the equation will equal 0. So, x=-2 means that when you substitute x=-2 into the quadratic equation, the equation equals 0; and similarly for x=6.
To create a quadratic equation with the solutions x = -2 and x = 6, we need to start by considering that the solutions of a quadratic equation occur when the equation equals zero.
So, let's set up the equation:
Let (x - α) and (x - β) be the factors of the quadratic equation, where α and β are the solutions of the equation.
From the given solutions, we have:
x = -2 and x = 6
To express these roots in terms of factors, we subtract them from x:
(x - (-2)) = 0
(x - 6) = 0
Now, to find the quadratic equation, we multiply these factors together:
(x + 2)(x - 6) = 0
Expanding this expression:
(x + 2)(x - 6) = x^2 - 6x + 2x - 12 = 0
So, the quadratic equation with the solutions x = -2 and x = 6 is:
x^2 - 4x - 12 = 0
A quadratic equation with given solutions x1 and x2 has the form:
(x-x1)(x-x2)=0
Here x1=-2, and x2=6.
Can you take it from here?