What is the answer to t2 plus t plus 3 equals 0?

Answer 1

If t2 + t + 3 = 0 then

[moving the 3 to the other side of the equation]

t2 + t = -3

[adding a value to both sides of the equation allowing us to easily factor the expression - i.e. completing the square]

t2 + t + 1/4 = -3 + 1/4

[factoring the expression: t2 + t + 1/4 factors to (t + 1/2) (t + 1/2) i.e. (t + 1/2)2 ]

(t + 1/2)2 = -3 + 1/4

(t + 1/2)2 = -2.75

[now square root each side]

t + 1/2 = -2.751/2

t = -2.751/2 - 1/2

[the square root of -2.75 is equal to the square root of 2.75 * the square root of -1. The square root of -1 is an imaginary number represented by the letter "i"]

t = (2.751/2 * -11/2) - 1/2

t = (2.751/2 * i) - 1/2

[the square root of 2.75 has two answers (+ and -) which will provide the two roots to the quadratic]

t = + or - 1.658i - 1/2 (to 3 decimal places only)

To solve this equation we have used the technique of "completing the square" and have made use of the imaginary number "i".

This equation does not have real roots as it involves the square root of a negative number and so this is the only way in which we can answer the question.