Question

Using the quadratic formula to solve x2 + 20 = 2x, what are the values of x?
a. 1+-/21 i
b.-1+-/19i
c. 1+-2/19i
d. 1+-/19i

Answer 1

To solve x^2 + 20 = 2x. First, we take all values to the left hand side and equate it to zero. x^2 - 2x + 20 = 0 The quadratic formular is given by x = (-b + or - sqrt(b^2 - 4ac)) / 2a, where: a = 1, b = -2 and c = 20 x = (-(-2) + or - sqrt((-2)^2 - (4 x 1 x 20))) / (2 x 1) = (2 + or - sqrt(4 - 80)) = (2 + or - sqrt(-76)) / 2 = (2 + or - 2sqrt(-19)) / 2 = 1 + or - sqrt(-19) = 1 + or - sqrt(19) i. Therefore, the solution to x^2 + 20 = 2x is x = 1 + or - sqrt(19) i (option d).

Answer 2

Answer:

The last option is the correct one

Explanation:

The general form of the quadratic equation is:

ax² + bx + c = 0

The given equation is:

x² + 20 = 2x

which can be rewritten as:

x² - 2x + 20 = 0

By comparison:

a = 1

b = -2

c = 20

The quadratic formula used to get the roots is shown in the attached image

We now substitute to get the roots as follows:

x = $\frac{2+\sqrt{(-2)^2-4(1)(20)}}{2(1)} = 1+\sqrt{19} i$

or x = $\frac{2-\sqrt{(-2)^2-4(1)(20)}}{2(1)} = 1-\sqrt{19} i$

Hope this helps :)