The imaginary number, i, is equal to the square root of negative one, √(-1). You may be wondering, though, what if the discriminant is less than zero? Can you take the square root of a negative number? The answer is yes, it simply requires the use of imaginary numbers. The one exception to this rule is if b^2 – 4ac (called the discriminant) equals zero, because the square root of zero only equals zero. Therefore, because the quadratic formula contains the square root of ( b² – 4ac), we must include the plus or minus in front, which results in two possible results for the square root and thus, two possible solutions to the quadratic equation. Therefore, whenever you take a square root of an expression, it is good practice to write +/- √ to express that there are two possible solutions. That is because two positive numbers multiplied together results in a positive number, but two negative numbers multiplied together also results in a positive number.įor example, the square root of 9 is plus or minus 3, because 3 x 3 = 9 and -3 x -3 = 9 as well. However, whenever one takes the square root of a positive value, there are always two possible answers, a positive answer and a negative answer. Popular Problems Graphing Calculator Calculators Cheat. During the derivation, one must take the square root in order to isolate x (recall √x² = x). Fractions Radical Equation Radical Factoring Inverse Quadratic Simplify. When y = 0 in a quadratic equation, deriving the solution for x results in the quadratic formula. X = \frac = -2 Why Are There Two Solutions to the Quadratic Equation?
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