Determine the discriminant for the quadratic equation -3 = x^2+4x+1 . Based on the discriminant value, how many real number solutions does the equation have?

Answer:1 realStep-by-step explanation:The discriminant is:[tex]b^2-4ac[/tex]which comes from the quadratic formula.The rules are:If the discriminant is > 0, there are 2 real solutionsIf the discriminant is = 0, there is 1 real solutionIf the discriminant is < 0, there are 2 imaginary solutions(there are 2 other situations involving square roots, but these are the most basic ones in Algebra 2 books when you study quadratics)First, we have to get that quadratic in standard form, which means getting everything on one side of the equals sign and setting it equal to 0:[tex]x^2+4x+4 = 0[/tex]where a = 1, b = 4, c = 4Filling in the discriminant:[tex]4^2-4(1)(4)[/tex]gives us 16 - 16 = 0Therefore, our quadratic has one real solution.  Factor it and see if you'd like, to prove that it is true.