determine the discriminant for the quadratic equation -3 = x²+4x + 1. based on the discriminant value, how…
determine the discriminant for the quadratic equation -3 = x²+4x + 1. based on the discriminant value, how many real number solutions does the equation have? discriminant = b² - 4ac\n0\n1\n2\n12
Answer
Explanation:
Step1: Rewrite the equation in standard form
First, rewrite $- 3=x^{2}+4x + 1$ as $x^{2}+4x+4 = 0$. Here, $a = 1$, $b = 4$, and $c = 4$.
Step2: Calculate the discriminant
Use the formula $\text{Discriminant}=b^{2}-4ac$. Substitute $a = 1$, $b = 4$, and $c = 4$ into the formula: $4^{2}-4\times1\times4=16 - 16=0$.
Step3: Determine the number of real - solutions
If the discriminant $\Delta=b^{2}-4ac = 0$, the quadratic equation has 1 real solution.
Answer:
1