Question

1.State all possible combination of roots (imaginaryand complex).2. Find all the roots (imaginary and complex). Stateall the roots

Answer 1

You have to see if the polynomial is factorable

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

In this case, it isn't, so now see the grade of the polynomial, we can see that is grade 2, so we can use the quadratic formula to find the roots:

`x=(-b\pm√(b^2-4ac))/(2a)`

the polynomial is in the form:

`ax^2+bx+c`

So, replace

`x=(-5\pm√(5^2-(4*10*-6)))/(2*10)=(-5\pm√(25+240))/(20)=(-5\pm√(265))/(20)`

So we have two imaginary roots

`x=(-5+√(265))/(20),\:x=(-5-√(265))/(20)`