Final answer:
The quadratic formula in standard form for a quadratic with roots at x = -7 + 7i and x = -7 - 7i, and a leading coefficient of 1 is y = (x - (-7 + 7i))(x - (-7 - 7i)).
Step-by-step explanation:
In this case, the quadratic equation has roots at x = -7 + 7i and x = -7 - 7i, and a leading coefficient of 1. To find the quadratic formula in standard form, we can use the fact that the roots of a quadratic equation are given by.
x = (-b ± √(b^2 - 4ac)) / 2a
Substituting the values into the formula, we have x = (-b ± √(b^2 - 4ac)) / 2a. Since the leading coefficient is 1, we have a = 1. The roots x = -7 + 7i and x = -7 - 7i can be written as x = -7 ± 7i. Plugging these values into the formula, we get:
x = (-b ± √(b^2 - 4ac)) / 2a
-7 ± 7i = (-b ± √(b^2 - 4ac)) / 2
The b term in the equation is 0, so plugging that in:
-7 ± 7i = (0 ± √(0 - 4ac)) / 2
Simplifying this, we get:
-7 ± 7i = ± √(- 4ac) / 2
-7 ± 7i = ± √(- 4c) / 2
Since the coefficient of c is -0.0211, we can write this as:
-7 ± 7i = ± √(- 4(-0.0211)) / 2
-7 ± 7i = ± √(0.0844) / 2
-7 ± 7i = ± 0.2908 / 2
Therefore, the quadratic formula in standard form with the given roots and leading coefficient is:
y = (x - (-7 + 7i))(x - (-7 - 7i))