A quadratic equation is generally given in the form of ax^2 + bx + c = 0, where a, b, and c are coefficients. In this case, the given quadratic equation is x^2 + 1.6x10^-2x - 1.6x10^-2 = 0, where
a = 1,
b = 1.6 x 10^-2, and
c = -1.6 x 10^-2.
The roots of the quadratic equation can be calculated using the quadratic formula, which is given by:
x = [-b ± sqrt(b^2 - 4ac)] / 2a
For the given equation, first let's calculate the discriminant which in the formula is represented as the part inside the square root: b^2 - 4ac.
Substituting the values:
Discriminant = (1.6 x 10^-2)^2 - 4*(1)*(-1.6 x 10^-2).
After the calculation, the discriminant value is approximately 0.06426.
Now, substituting these values into the quadratic formula, we can find the roots of the equation. Let's start with the root calculation for the positive square root in the formula:
Root1 = [- (1.6 x 10^-2) + sqrt(0.06426)] / 2*(1).
This gives the first root approximately equal to 0.11874.
Next, let's calculate using the negative square root in the formula:
Root2 = [- (1.6 x 10^-2) - sqrt(0.06426)] / 2*(1).
This provides the second root approximately equal to -0.13474.
So, the roots of the given quadratic equation x^2 + 1.6x10^-2x - 1.6x10^-2 = 0 are
x = 0.11874 and x = -0.13474. These roots mean that if we substitute these values into the original equation for x, the total sum will equal zero. This is evidence we have found the correct roots for this particular quadratic equation.