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How do you do square root math problems?
That will obviously depend on the specific problem. If you have an equation with a variable under a square root sign, it often helps to square both sides of the equation.
What is the expression b2-4ac under the radical sign in the quadratic formula?
6
How do you find the discriminant on a graph?
The discriminant is the expression under the square root of the quadratic formula.For a quadratic equation: f(x) = ax2 + bx + c = 0, can be solved by the quadratic formula:x = (-b +- sqrt(b2 - 4ac)) / (2a).So if you graph y = f(x) = ax2 + bx + c, then the values of x that solve [ f(x)=0 ] will yield y = 0. The discriminant (b2 - 4ac) will tell you something about the graph.(b2 - 4ac) > 0 : The square root will be a real number and the root of the equation will be two distinct real numbers, so the graph will cross the x-axis at two different points.(b2 - 4ac) = 0 : The square root will be zero and the roots of the equation will be a real number double root, so the graph will touch the x-axis at only one points.(b2 - 4ac) < 0 : The square root will be imaginary, and the roots of the equation will be two complex numbers, so the graph will not touch the x-axis.So by looking at the graph, you can tell if the discriminant is positive, negative, or zero.
Explain the conditions under which a quadratic equation can be solved using simple rearrangement versus using the quadratic formula?
The quadratic formula always works (as long as one considers complex numbers). "Simple rearrangement" may be quicker when the numbers look simple enough for you to decide (or rather guess) what the factors/ roots are by inspection (but the "rearrangement" method still works -- the numbers may just be more complicated). Probably the easiest quadratic is when the coefficient of x is zero (i.e. a polynomial of the form ax^2+b=0) or when there is no constant term (i.e. ax^2+bx=0) The quadratic formula cannot be used to solve an equation if a term in the equation has a degree higher than 2 (or if it can't be put in the form ax^2+bx+c=0). There are other more complex formulas for polynomials for degree 3 and 4.
What is the number under the square root sign called?
radicand
What is the number called under the square root when the number is negative in the quadratic equation?
The term inside the square root symbol is called the radicand. There isn't a specific term for it based on its sign; whether it's positive or negative, it's still the radicand.I'm a little confused by your reference to the quadratic equation.If the radicand is negative, the root is an imaginary number, though that doesn't specifically have anything to do with the quadratic equation in particular.If the quantity b2 - 4ac is negative in the quadratic equation, the root of the quadratic equation is either complex or imaginary depending on whether or not b is zero.---------------------------Thank you to whoever answered this first; you saved me a bit of trouble explaining this to the asker :)However, in the quadractic equation, the number under the radical is called the discriminant. This determines the number of solutions of the quadratic. If the radicand is negative, this means that there are no real solutions to the equation.
What determines the nature of the roots of a quadratic equation?
The determinant.The determinant is the part under the square root of the quadratic equation and is:b2-4ac where your quadratic is of the form: ax2+bx+cIf the determinant is less than zero then you have 'no real solutions' (as the square root of a negative number is imaginary.)If the determinant is = 0, then you have one real solution (because you can discount the square root of the quadratic equation)If the determinant is greater than zero you have two real solutions as you have (-b PLUS OR MINUS the square root of the determinant) all over 2aTo find the solutions where they exist you'll need to solve the quadratic formula or use another method.
The degree of a quadratic equation?
The Quadratic Formula song: (my grade saver) To the tune of the jack in the box song X equals negative B plus or minus square root of B squared minus 4AC all over 2A :)
What is the nature of zeros in quadratic function?
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...
Can a graphing calculator be used to solve any quadratic equation?
For the most part it can. if you have a TI-83 or better, you can use the solver under your math button. All you have to do is plug in the equation that is set to equal zero!
How do you do square root math problems?
That will obviously depend on the specific problem. If you have an equation with a variable under a square root sign, it often helps to square both sides of the equation.
How do you determine the number of real solutions to a quadratic equation?
Put the equation in the form ax2 + bx + c = 0. Replace a, b, and c in the quadratic formula: x = (-b (plus-or-minus) root(b2 - 4ac)) / 2a. Look at the term under the radical sign, which I wrote as "root" here. If b2 - 4ac is...Positive: the equation has two real solutions.Zero: the equation has one ("double") solution.Negative: the equation has two complex solutions (and therefore no real solution).
What is the expression b2-4ac under the radical sign in the quadratic formula?
6
How many times will The graph of a quadratic function crosses the x-axis twice?
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.
How do you find the discriminant on a graph?
The discriminant is the expression under the square root of the quadratic formula.For a quadratic equation: f(x) = ax2 + bx + c = 0, can be solved by the quadratic formula:x = (-b +- sqrt(b2 - 4ac)) / (2a).So if you graph y = f(x) = ax2 + bx + c, then the values of x that solve [ f(x)=0 ] will yield y = 0. The discriminant (b2 - 4ac) will tell you something about the graph.(b2 - 4ac) > 0 : The square root will be a real number and the root of the equation will be two distinct real numbers, so the graph will cross the x-axis at two different points.(b2 - 4ac) = 0 : The square root will be zero and the roots of the equation will be a real number double root, so the graph will touch the x-axis at only one points.(b2 - 4ac) < 0 : The square root will be imaginary, and the roots of the equation will be two complex numbers, so the graph will not touch the x-axis.So by looking at the graph, you can tell if the discriminant is positive, negative, or zero.
When the discriminant is a perfect square are the solutions rational or irrational?
The "discriminant" here refers to the part of the quadratic equation under the radical (square root) sign. When it is a perfect square, the square root is also a perfect square, so the radical goes away, leaving only rational numbers. So, when the discriminant is a perfect square, the solutions are (usually) rational. Unless, of course, some other part of the result is irrational. For example, if the coefficient of the x2 term ("a" in the quadratic formula) is pi, and the constant term is 1/pi, the discriminant will turn out to be 4 (4ac = 4 * pi * 1/pi = 4), which is a perfect square, but solutions will be irrational anyway because the denominator becomes 2pi, and pi is irrational.
How to tell if there are no real roots?
The real roots of what, exactly? If you mean a square trinomial, then: If the discriminant is positive, the polynomial has two real roots. If the discriminant is zero, the polynomial has one (double) real root. If the discriminant is negative, the polynomial has two complex roots (and of course no real roots). The discriminant is the term under the square root in the quadratic equation, in other words, b2 - 4ac.
