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What is the Discriminant?

What is the discriminant?

Summary

  1. The symbol over the b2-4ac is called a 'radical', or a square root symbol
  2. '±' means 'plus or minus'
  3. The DISCRIMINANT is the expression under the radical
  4. The 'a', 'b', and 'c' values come from the general form of a quadratic equation: ax2+bx+c=0
  5. 'a' is 5, the number in front of x2
  6. 'b' is 3, the number in front of x
  7. 'c' is 1, the constant term
  8. Since the discriminant is a negative number, -11, this equation has two complex solutions

Notes

    1. Real numbers are all numbers that can be found on a number line
    2. Before Algebra 2, we were only working with real numbers
    1. Complex numbers include imaginary numbers as well as real numbers
    2. Since we now know what imaginary and complex numbers are, we have a slightly different definition for the discriminant
    1. Remember, we originally found the discriminant from the Quadratic Formula
    2. It's still the same expression that it was before!
    3. The discriminant is the expression under the radical, or square root sign, in the Quadratic Formula: b2-4ac
    4. The 'a', 'b', and 'c' values come from the general form of a quadratic equation: ax2+bx+c=0
    1. Again, this is just like how we learned the discriminant before
    2. But this time, we need to account for complex solutions
    1. When we have a positive discriminant, we're taking the square root of a positive number, which is a real number
    2. But we also have a plus or minus in front of the square root, so we get two real solutions
    3. If the discriminant is 0, we're taking the square root of 0, which is 0
    4. We get the same value whether we add or subtract 0, so we have one real solution
    5. When we have a negative discriminant, we're taking the square root of a negative number, which is an imaginary number
    6. Since we're adding and subtracting an imaginary number, we will have two complex solutions
    1. The 'a', 'b', and 'c' values in the discriminant come from the general form of a quadratic equation
    2. 'a' is the coefficient in front of x2, which is 5
    3. 'b' is the coefficient in front of x, which is 3
    4. 'c' is the constant term, which is 1
    1. This means we will have a negative number under the square root in the Quadratic Formula
    1. Since our discriminant is -11, that gives us a negative number under the square root
    2. The square root of a negative number is an imaginary number
    3. Since that means we'll be adding and subtracting an imaginary number, we will have two complex solutions