The discriminant.
discriminant
6
Suppose the expression under the radical sign is y. Then the first step is to simplify y. Next find a term (or expression) x, such that y = x^2*z for some term (or expression) z. Then x*sqrt(z) is a simplification of sqrt(y).
Radicand
"Radical x times radical x" could be interpreted as the square root of x times the square root of x - in which case the product would be x (the number under the radical sign)
discriminant
The discriminant
6
radicand
If the discriminant - the part under the radical sign in the quadratic formula - is negative, then the result is complex, it is as simple as that. You can't convert a complex number to a real number. If a particular problem requires only real-number solutions, then - if the formula gives complex numbers - you can state that there is no solution.
No, you cannot add or subtract under the radical. The radical represents the square root function, and it only operates on the number or expression that is inside the radical. To add or subtract, you need to simplify the expressions inside the radical first.
A radical expression is considered to be in simplified form when there are no perfect square factors (or higher-order factors, depending on the root) remaining under the radical, and no fractions exist within the radical itself. Additionally, any coefficients in front of the radical should be as simple as possible, and the index of the radical should be minimal. If these conditions are met, the expression is deemed simplified.
A quadratic function can have up to two roots. Depending on the discriminant (the expression under the square root in the quadratic formula), it can have two distinct real roots, one repeated real root, or no real roots at all (in which case the roots are complex). Therefore, the total number of roots, considering both real and complex, is always two.
The details depend on the specific radical expression. Normally, you'll want to: * Avoid a perfect square under a radical sign. Take it out, by separating the radical into two parts. Example: root (x squared y) = root (x squared) x root (y) = x root (y). * Avoid a radical sign in the denominator. If you multiply numerator and denominator by the same square root, you get an expression in which there are roots in the numerator, but not in the denominator.
Suppose the expression under the radical sign is y. Then the first step is to simplify y. Next find a term (or expression) x, such that y = x^2*z for some term (or expression) z. Then x*sqrt(z) is a simplification of sqrt(y).
Only if the term under the radical (square root sign) can be simplified to a rational expression. For example, √(4x2).
To insert a quadratic formula (or any other scientific formula) into a Word document, go toInsert (tab) > Equations (under the Symbols block)From there you can either select the format of the formula you would like to insert if a template is available (there is a template already for quadratic equations) but if there isn't one, can either download on from Office.com OR create your own by clicking Insert New Equation.