Question

1. State all possible combination of roots (imaginaryand complex).2. Find all the roots (imaginary and complex). Stateall the roots10x^2 + 5x - 6 = 0

Answer 1

Given:

There is a quadratic equation given as below

`10x^2+5x-6=0`

Required:

We need to find all the roots of given equation

Step-by-step explanation:

There are two roots of given equation because there is mamimum power 2

To find roots

compare given equation with

`ax^2+bx+c=0`

by this we get

`\begin{gathered} a=10 \\ b=5 \\ c=-6 \end{gathered}`

Now solve with the quadratic formula

`x_(1,2)=(-b\pm√(b^2-4ac))/(2a)`

plug all the values

`\begin{gathered} x_(1,2)=(-5\pm√(25-4*10*(-6)))/(2*10) \\ \\ x_(1,2)=(-5\pm√(25+240))/(20) \\ \\ x_(1,2)=(-5\pm√(265))/(20) \end{gathered}`

Final answer:

Roots of given equation is

`x_(1,2)=(-5\pm√(265))/(20)`