Calculator Soup Quadratic (2024)

FAQs

Are there 2 answers for the quadratic formula? ›

Solving the quadratic equation. A quadratic equation with real or complex coefficients has two solutions, called roots. These two solutions may or may not be distinct, and they may or may not be real.

As we have seen, there can be 0, 1, or 2 solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b² - 4ac), is positive, negative, or zero. This expression has a special name: the discriminant.

Check your answers to a quadratic equation by reworking them into the original equation and seeing if they equal 0. Write the quadratic equation and the roots that you calculated. For example, let the equation be x² + 3x + 2 = 0, and the roots be -1 and -2. Substitute the first root into equation and solve.

If b² - 4ac is positive (>0) then we have 2 solutions. If b² - 4ac is 0 then we have only one solution as the formula is reduced to x = [-b ± 0]/2a. So x = -b/2a, giving only one solution. Lastly, if b² - 4ac is less than 0 we have no solutions.

Answer: If a quadratic equation has exactly one real number solution, then the value of its discriminant is always zero. A quadratic equation in variable x is of the form ax² + bx + c = 0, where a ≠ 0.

Are you referring to the signs on the terms in a quadratic equation. In general, however, ALL quadratic equations will have two solutions. Often they are both real and might be both positive, both negative, or one positive and one negative. Sometimes one or both of the solutions will be complex (i, sqrt[-1]).

The prefix quad means “four” and quadratic expressions are ones that involve powers of x up to the second power, not the fourth power.

Factoring is the first of the three methods of solving quadratic equations. It is often the fastest way to solve a quadratic equation, so usually should be attempted before any other method. This method relies on the fact that if two expressions multiply to zero, then at least one of them must be zero.

The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula: (-b±√(b²-4ac))/(2a) . See examples of using the formula to solve a variety of equations.

Answer: There are various methods by which you can solve a quadratic equation such as: factorization, completing the square, quadratic formula, and graphing. These are the four general methods by which we can solve a quadratic equation.

How to simplify quadratic equations? ›

Step 1: Using inverse operations, move all terms to one side of your equal sign. Step 2: Simplify your equation, and move terms around so that your equation is in the standard form of a quadratic function. Step 3: Now that your equation is in standard form, you can determine the values for a, b, and c.

The discriminant formula is used to determine the nature of the roots of a quadratic equation. The discriminant of a quadratic equation ax² + bx + c = 0 is D = b² - 4ac. If D > 0, then the equation has two real distinct roots. If D = 0, then the equation has only one real root.

The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula: (-b±√(b²-4ac))/(2a) .

All quadratic equations of the form ax^2 + bx + c have precisely two roots (solutions) and no more. The discriminant, D = (b^2 - 4ac), tells you what types of roots they are. If D is positive, then there two real roots.

Quadratic equations can have at most two solutions. The number of solutions are not fixed to 2, it can also be none, unique, or two solutions. The given statement is False. Quadratic equations are not fixed to two real solutions, there can be two, one, or no real solutions at all.