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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.
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A quadratic is a second degree polynomial of the form: ax2 + bx + c 0 where a 0. 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. This quadratic equation root calculator lets you find the roots or zeroes of a quadratic equation. Next, identify the relevant information, define the variables, and plan a strategy for solving the problem. Therefore, whenever you take a square root of an expression, it is good practice to write +/- √ to express that there are two possible solutions. To solve math problems step-by-step start by reading the problem carefully and understand what you are being asked to find. The Quadratic Formula Calculator finds solutions to quadratic equations with real coefficients. 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. Symbolab is the best step by step calculator for a wide range of physics problems, including mechanics, electricity and magnetism, and thermodynamics. Step 1: Enter the equation you want to solve using the quadratic formula. However, whenever one takes the square root of a positive value, there are always two possible answers, a positive answer and a negative answer. During the derivation, one must take the square root in order to isolate x (recall √x² = x). 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?