How many solutions does 4x^2 + 8x + 3 = 0 have?

1 Answer
May 1, 2015

The easiest way to determine the answer to your question is to evaluate the color(red)("discriminant")
For a quadratic in the form:
y = ax^2+bx+c
the color(red)("discriminant") is equal to
color(red)(b^2-4ac)

For your example
4x^2+8x+3=0
The color(red)("discriminant") is
Delta = (8^2-4(4)(3))/(2(4))

Delta=2

The number of solutions is determined by the value of the color(red)("discriminant, " Delta)

Delta { (>0 " two solutions"),(=0" one solution"),(<0" no solutions"):}

So
4x^2+8x+3=0 has two solutions

Further explanation:
The discriminant comes from the formula for quadratic root solutions
(-b+-sqrt(color(red)(b^2-4ac)))/(2a)
and it should be fairly obvious from this to understand why

color(red)(b^2-4ac) { (>0 rarr" two solutions"),(=0 rarr" one solution"),(<0 rarr " no solutions"):}