Sure, I can help with that.
A quadratic equation is given by the formula: ax^2 + bx + c = 0
If a quadratic equation with roots r1 and r2, it can be written in the factored form as follows:
(x - r1) (x - r2) = 0
In our case, the roots of the quadratic equation are given as 8 and 11. Plugging these values into our factored equation form, we get:
(x - 8) (x - 11) = 0
Next, we need to expand this equation to get the quadratic equation in its standard form.
We do this by using the distributive law of multiplication which states: a(b + c) = ab + ac. Applying the law to both parts of our equation gives us:
x * x - x * 11 - 8 * x + 8 * 11 = 0,
Simplifying the equation leads to:
x^2 - 11x - 8x + 88 = 0.
Finally, combine like terms to get our quadratic equation in standard form:
x^2 - 19x + 88 = 0.
Therefore, the quadratic equation with roots 8 and 11 is x² - 19x + 88 = 0.