• The value of the discriminant ,D= -16
,• The solution to the quadratic equation is
[tex]x=\frac{1+2i}{5}\text{ or }\frac{1-2i}{5}[/tex]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;
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]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;
[tex]x=\frac{-(-2)\pm\sqrt[]{-16}}{2(5)}[/tex]Note that:
√-1 = i
[tex]x=\frac{2\pm\sqrt[]{16\times-1}}{10}[/tex][tex]x=\frac{2\pm\sqrt[]{16}\times\sqrt[]{-1}}{10}[/tex][tex]x=\frac{2\pm4i}{10}[/tex][tex]x=\frac{2}{10}\pm\frac{4i}{10}[/tex][tex]x=\frac{1}{5}\pm\frac{2}{5}i[/tex][tex]x=\frac{1\pm2i}{5}[/tex]That is;
[tex]\text{Either x=}\frac{1+2i}{5}\text{ or x=}\frac{1-2i}{5}[/tex]