We must work backwards. When we are given the roots, we take the opposite of the roots, (therefore, we multiply it by -1) and then we combine it with x and multiply it by the other roots. If you're confused, here's an example:
roots 6, -3 and 2:
opposite of 6
-6
(x-6)
opposite of 2
-2
(x-2)
opposite of -3
3
(x+3)
Then we multiply them:
(x-6)(x-2)(x+3)
Then, we would multiply all of those using foil. But, that is just an example.
Here's the real thing:
opposite of 0
-0
(x-0)
using the identity property of addition, this simplifies to
x
opposite of 3
-3
(x-3)
multiply them:
x(x-3)
Because there is only 1 term on the outside, we don't need to use foil or anything like that. All we have to do is distribute:
x(x)+x(-3)
[tex] x^{2} -3x[/tex]
Now, the question asks for a quadratic equation
if it were asking for a function, we would make that equal to the variable
y
But, it is asking for an equation.
The way you find roots is that you set the y from the function to 0
So we will do the same and set the expression to 0, making it an equation. Final answer:
[tex] x^{2} -3x=0[/tex]
sorry it's so long, but I hope I helped!
