Determine the discriminant for the quadratic equation -3 = x^2 + 4x + 1. Based on the discriminant value, how many real number solution does the equation have?
Discriminant =b^2 - 4ac
Ah, the quadratic equation, my old nemesis! Let's see. The equation you provided is -3 = x^2 + 4x + 1. To determine the discriminant, we use the formula Discriminant = b^2 - 4ac.
In this case, a = 1, b = 4, and c = 1. Plugging these values into the formula, we get:
Discriminant = (4)^2 - 4(1)(1) = 16 - 4 = 12.
Now, based on the discriminant value of 12, let's ask ourselves a question: How many real number solutions does this equation have? Drumroll, please... 🥁
The discriminant is positive, which means we have TWO real number solutions! So, hold on to your clown hat, because this equation is going to give us double the fun!
To determine the discriminant for the quadratic equation -3 = x^2 + 4x + 1, we need to compare it with the standard form of a quadratic equation: ax^2 + bx + c = 0.
In this case, a = 1, b = 4, and c = 1. Now we can use the formula for the discriminant:
Discriminant = b^2 - 4ac
Substituting the values, we get:
Discriminant = (4)^2 - 4(1)(1)
= 16 - 4
= 12
Therefore, the discriminant is 12.
To determine the number of real number solutions the equation has, we can use the discriminant value.
If the discriminant is positive (greater than 0), the quadratic equation will have two distinct real number solutions.
If the discriminant is zero, the quadratic equation will have one real number solution (often referred to as a double root).
If the discriminant is negative (less than 0), the quadratic equation will have no real number solutions and will have two complex conjugate solutions.
In our case, since the discriminant is 12 (which is positive), the quadratic equation has two distinct real number solutions.
-3 = x^2 + 4x + 1
x^2 + 4x + 4 = 0 , so a=1, b=4, and c=4
just plug it in.