Question

Which two values of x are roots of the polynomial below?
x2 + 5x+7

Answer 1

The roots are

`x=(-5+i√(3))/(2)` and
`x=(-5-i√(3))/(2)`

Explanation:

we have

`x^(2) +5x+7`

To find the roots equate the polynomial to zero and cmplete the square

`x^(2) +5x+7=0`

`x^(2) +5x=-7`

`(x^(2) +5x+2.5^(2))=-7+2.5^(2)`

`(x^(2) +5x+6.25)=-0.75`

rewrite as perfect squares

`(x+2.5)^(2)=-0.75`

take square root both sides

`(x+2.5)=(+/-)\sqrt{-(3)/(4)}`

Remember that

`i=√(-1)`

substitute

`(x+2.5)=(+/-)i\sqrt{(3)/(4)}`

`(x+(5)/(2))=(+/-)i(√(3))/(2)`

`x=-(5)/(2)(+/-)i(√(3))/(2)`

therefore

The roots are

`x=(-5+i√(3))/(2)`

`x=(-5-i√(3))/(2)`