Question

What is the soulution of the fallowing equation X^2+3x+4=0

Answer 1

`x = (-3)/(2) + i(\sqrt7)/(2)\ \text{and }(-3)/(2)-i(\sqrt7)/(2)`

Explanation:

To solve this equation, we need to use the quadratic formula.

The quadratic formula is:

`x = (-b\ \pm\ √(b^2-4ac) )/(2a)`

For the quadratic equation ax² + bx + c = 0. If x² + 3x + 4 = 0 is the given equation, then...

a = 1, b = 3, and c = 4

Since we now know all our variables, we can plug them into the equation, and solve for x.

Solving for X

`x = (-b\ \pm\ √(b^2-4ac) )/(2a)`

`x = (-3\ \pm\ √(3^2-4(1)(4)) )/(2(1))`

`x = (-3\ \pm\ √(9-16) )/(2)`

`x = (-3\ \pm\ √(-7) )/(2)`

We cannot take the square root of a negative number. However, we can use imaginary number i to represent the square root of -1.

Therefore:

`x = (-3\ \pm\ i√(7) )/(2)` OR
`x = (-3)/(2) + i(\sqrt7)/(2)\ \text{and }(-3)/(2)-i(\sqrt7)/(2)`