Explanation:
This graph shows a quadratic curve with roots 0 and -4
The polynomial is therefore
x² -x(α+β) + αβ
x² -x(0-4) + 0(-4)
x² +4x +0
x² + 4x
But it's an n-shaped curve, meaning a is negative
Multiply through by -1
-x² - 4x
y = -x² - 4x
So when the input value y = 3, we have
3 = -x² - 4x
Rearrange
x² + 4x + 3 = 0
Factorize
x² + 3x + x + 3 = 0
x(x + 3) +1(x + 3) = 0
(x + 1) (x + 3) = 0
x + 1 = 0 and x + 3 = 0
x = 0-1 and x = 0-3
Therefore,
x = -1 and -3
Check the graph to confirm