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.
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.
Nature Of The Zeros Of A Quadratic Function The quantity b2_4ac that appears under the radical sign in the quadratic formula is called the discriminant.It is also named because it discriminates between quadratic functions that have real zeros and those that do not have.Evaluating the discriminant will determine whether the quadratic function has real zeros or not. The zeros of the quadratic function f(x)=ax2+bx+c can be expressed in the form S1= -b+square root of D over 2a and S2= -b-square root of D over 2a, where D=b24ac.... hope it helps... :p sorry for the square root! i know it looks like a table or something...
A quadratic function will cross the x-axis twice, once, or zero times. How often, depends on the discriminant. If you write the equation in the form y = ax2 + bx + c, the so-called discriminant is the expression b2 - 4ac (it appears as part of the solution, when you solve the quadratic equation for "x" - the part under the radical sign). If the discriminant is positive, the x-axis is crossed twice; if it is zero, the x-axis is crossed once, and if the discriminant is negative, the x-axis is not crossed at all.