The correct answer is or. Using the formula,. If you forget that the denominator is under both terms in the numerator, you might get or. However, the correct simplification is , so the answer is or. The Discriminant. These examples have shown that a quadratic equation may have two real solutions, one real solution, or two complex solutions.
In the Quadratic Formula, the expression underneath the radical symbol determines the number and type of solutions the formula will reveal. You can always find the square root of a positive, so evaluating the Quadratic Formula will result in two real solutions one by adding the positive square root, and one by subtracting it. There will be one real solution. Since you cannot find the square root of a negative number using real numbers, there are no real solutions.
However, you can use imaginary numbers. You will then have two complex solutions, one by adding the imaginary square root and one by subtracting it.
Use the discriminant to determine how many and what kind of solutions the quadratic equation. Evaluate b 2 — 4 ac. The result is a negative number. The discriminant is negative, so the quadratic equation has two complex solutions. Suppose a quadratic equation has a discriminant that evaluates to zero.
Which of the following statements is always true? A The equation has two solutions. B The equation has one solution. C The equation has zero solutions. A discriminant of zero means the equation has one solution.
When the discriminant is zero, the equation will have one solution. Applying the Quadratic Formula. Quadratic equations are widely used in science, business, and engineering. Quadratic equations are commonly used in situations where two things are multiplied together and they both depend on the same variable.
For example, when working with area, if both dimensions are written in terms of the same variable, you use a quadratic equation. Because the quantity of a product sold often depends on the price, you sometimes use a quadratic equation to represent revenue as a product of the price and the quantity sold.
Quadratic equations are also used when gravity is involved, such as the path of a ball or the shape of cables in a suspension bridge. A very common and easy-to-understand application is the height of a ball thrown at the ground off a building. Because gravity will make the ball speed up as it falls, a quadratic equation can be used to estimate its height any time before it hits the ground.
Note: The equation isn't completely accurate, because friction from the air will slow the ball down a little. For our purposes, this is close enough. A ball is thrown off a building from feet above the ground. The negative value means it's heading toward the ground. About how long does it take for the ball to hit the ground?
When the ball hits the ground, the height is 0. Substitute 0 for h. This equation is difficult to solve by factoring or by completing the square, so solve it by applying the Quadratic Formula,. In this case, the variable is t rather than x. Be very careful with the signs.
Use a calculator to find both roots. Consider the roots logically. The other solution, 3. The ball hits the ground approximately 3. The area problem below does not look like it includes a Quadratic Formula of any type, and the problem seems to be something you have solved many times before by simply multiplying. But in order to solve it, you will need to use a quadratic equation. Bob made a quilt that is 4 ft x 5 ft. He has 10 sq.
Mar 9, Explanation: The discriminant indicated normally by Delta , is a part of the quadratic formula used to solve second degree equations. I hope that helps! George C. Dec 5, See explanation Explanation: The discriminant of a polynomial equation is a value computed from the coefficients which helps us determine the type of roots it has - specifically whether they are real or non-real and distinct or repeated. It has a complex conjugate pair of non-real roots. It may have one real root of multiplicity 3.
Otherwise it may have two distinct real roots, one of which is of multiplicity 2. Then, the roots of the quadratic equation are real and equal. Then, the roots of the quadratic equation are not real and unequal. In this instance, the roots amount to be imaginary. Then, the roots of the quadratic equation are unequal, real, and rational. It is absolutely necessary that the arrangement of the equation is made in a correct manner, else solution cannot be arrived at.
Keep an eye out for negative b 2. Since it cannot be negative, be sure to change it to positive. The square of either positive or negative will always be positive. Watch out for two solutions.
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