Question

How do you find the discriminant and how many and what type of solutions does `x^2 +4x +4=0` have?

Answer 1

discriminant `D= b^2 - 4ac`

we have equation :
`x^2 + 4x + 4 = 0`

here:
`a =1`
`b = 4`
`c = 4`
(the coefficients of `x^2` , `x` and the constant term respectively)

finding `D`:

`D= b^2 - 4ac = (4^2) - (4 xx 1 xx 4)`
`D= 16 - 16 = 0`

formula for roots :
`x = (-b +- sqrt D) / (2a)`
`x = (-4 +- sqrt 0) / (2 xx 1)`
`x = (-4 + 0) / 2 and (-4 - 0) /2`
`x` has two equal solutions:
`x = -2`

the solutions are real and equal as `D=0`