Question

What are the solutions of the polynomial 4x^2-4x+10? Write the answer in complex, a+bi form

Answer 1

Step-by-step explanation:

The expression is given below as

`4x^2-4x+10=0`

To find the solution, we will use the quadratic formula below

`\begin{gathered} x_(1.2)=(-b\pm√(b^2-4ac))/(2a) \\ where, \\ a=4,b=-4,c=10 \end{gathered}`

By substituign the values, we will have

`\begin{gathered} x_(1.2)=(-b\pm√(b^2-4ac))/(2a) \\ x_(1.2)=(-(-4)\pm√((-4)^2-4(4*10)))/(2*4) \\ x_(1.2)=(4\pm√(16-160))/(8) \\ x_(1.2)=(4\pm√(-144))/(8) \\ recall√(-144)=12i \\ x_(1.2)=(4\pm12i)/(8) \\ x_1=(4)/(8)+(12i)/(8),x_2=(4)/(8)-(12i)/(8) \\ x_1=(1)/(2)+(3)/(2)i,x_2=(1)/(2)-(3)/(2)i \end{gathered}`

Hence,

The final answer is

`x_=(1)/(2)+(3)/(2)\imaginaryI\text{ }or\text{ }x=(1)/(2)-(3)/(2)\imaginaryI`