Question

Solving Quadratic Equations with Complex SolutionsThe discriminant: D=b^2-4acQuestion:5x^2-2x+1=0

Answer 1

• The value of the discriminant ,D= -16

,

• The solution to the quadratic equation is

`x=(1+2i)/(5)\text{ or }(1-2i)/(5)`

Step - by - Step Explanation

What to find?

• The discriminant d= b² - 4ac

,

• The solution to the quadratic equation.

Given:

5x² - 2x + 1=0

Comparing the given equation with the general form of the quadratic equation ax² + bx + c=0

a=5 b=-2 and c=1

Uisng the quadratic formula to solve;

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

The discriminant D=b² - 4ac

Substitute the values into the discriminant formula and simplify.

D = (-2)² - 4(5)(1)

D = 4 - 20

D = -16

We can now proceed to find the solution of the quadratic equation by substituting into the quadratic formula;

`x=\frac{-(-2)\pm\sqrt[]{-16}}{2(5)}`

Note that:

√-1 = i

`x=\frac{2\pm\sqrt[]{16*-1}}{10}`

`x=\frac{2\pm\sqrt[]{16}*\sqrt[]{-1}}{10}`
`x=(2\pm4i)/(10)`
`x=(2)/(10)\pm(4i)/(10)`
`x=(1)/(5)\pm(2)/(5)i`
`x=(1\pm2i)/(5)`

That is;

`\text{Either x=}(1+2i)/(5)\text{ or x=}(1-2i)/(5)`