MATH SOLVE

2 months ago

Q:
# WeeeeeBeeSEGEDESELEBESEDEESESPSSolve for x using the quadratic formula.x2 - 2x+5 = 0β

Accepted Solution

A:

Answer:In the set of real numbers, the equation has no solution.In the set of complex numbers the solutions are:1 - 2i and 1 + 2iStep-by-step explanation:[tex]\text{The quadratic formula of a quadratic equation}\ ax^2+bx+c=0:\\\\\text{if}\ b^2-4ac<0,\ \text{then an equation has no real solution}\\\\\text{if}\ b^2-4ac=0,\ \text{then an equation has one solution}\ x=\dfrac{-b}{2a}\\\\\text{if}\ b^2-4ac>0,\ \text{then an equation has two solutions:}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex][tex]\text{We have the equation:}\ x^2-2x+5=0\\\\a=1,\ b=-2,\ c=5\\\\\text{Substitute:}\\\\b^2-4ac=(-2)^2-4(1)(5)=4-20=-16<0\\\\\bold{NO\ REAL\ SOLUTION}[/tex][tex]\text{If you want the complex solution, then:}\\\\i=\sqrt{-1}\\\\\text{Therefore}\ \sqrt{-16}=\sqrt{(16)(-1)}=\sqrt{16}\cdot\sqrt{-1}=4i\\\\x=\dfrac{-(-2)\pm4i}{2(1)}=\dfrac{2\pm4i}{2}=1\pm2i[/tex]