What are the roots of the polynomial x2 plus 5x plus 11?

Answer 1

We need to use the quadratic formula for this.

-b±√(b2-4ac)

-----------------

2a

Let me explain some of the symbols and letters first.

±- is the plus or minus sign. You will perform both separately when we reach this step.

√-is the square root sign.

The line above 2a is the division line.

The letter a represents the quantity of x2, which is 1 in this case

The letter b represents the quantity of x, which is 5 in this case

The letter c represents the quantity of 1, which is 11 in this case

Let's plug the numbers in.

-5±√(52-4(1)(11))

-----------------

2(1)

Solve:

-5±√(52-4(1)(11))

----------------------- =

2(1)

-5±√((25)-(44))

----------------------- =

2

-5±√((25)-(44))

----------------------- =

2

-5±√(-19)

----------------------- =

2

We cannot have a square root of a negative, so this polynomial is not able to be solved if we restrict ourselves to the real numbers. However, we certainly have two complex roots.