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

Answer 1

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"):}#

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Answer 2

Savannah Anderson

The quadratic equation 4x^2 + 8x + 3 = 0 has two solutions.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.