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:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

the polynomial is in the form:

$ax^2+bx+c$

So, replace

$x=\frac{-5\pm\sqrt{5^2-(4*10*-6)}}{2*10}=\frac{-5\pm\sqrt{25+240}}{20}=\frac{-5\pm\sqrt{265}}{20}$

So we have two imaginary roots

$x=\frac{-5+\sqrt{265}}{20},\:x=\frac{-5-\sqrt{265}}{20}$