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

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

$x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

plug all the values

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

Final answer:

Roots of given equation is

$x_{1,2}=\frac{-5\pm\sqrt{265}}{20}$