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In the quadratic formula, you have -b +- square root of ( b^2 - 4ac) all over 2a. There are three cases:
No values:
If the discriminant is negative, the square root of b^2 -4ac has no values, because we cannot take the square root of a negative number.
One value:
If it is zero, than the square root is also zero. This means that there is one solution because +- 0 is always just 0. (-b+-0)/2a only has one value.
2 values:
if the discriminant is positive then it has a square root. BUT, there is a difference between here and the last step. (-b +- discriminant )/ 2a has 2 values: one for the positive and one for the negative.
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Minor amendment:
-b +- square root of ( b^2 - 4ac) all over 2a is the quadratic formula.
The discriminant is simply b2 - 4ac
If b2 - 4ac > 0 then there are two distinct real roots to the quadratic;
If b2 - 4ac = 0 then there is one real roots to the quadratic (or two identical roots);
If b2 - 4ac < 0 then there are no real roots to the quadratic.
The values of the roots are exactly as described in the earlier answer.
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What is the discriminant to determine how many real number solutions the quadratic equation -4j2 plus 3j-28 equals 0 has?
The discriminant is -439 and so there are no real solutions.
What is true of the discriminant when the two real number solutions to a quadratic equation are rational numbers?
The discriminant must be a perfect square or a square of a rational number.
What is a discriminant and how does help to solve equations?
In the quadratic formula, the discriminant is b2-4ac. If the discriminant is positive, the equation has two real solutions. If it equals zero, the equation has one real solution. If the discriminant is negative, it has two imaginary solutions. This is because you find the square root of the discriminant and add or subtract it from -b and divide the sum or difference by 2a. If the square root is of a positive number, then you get two different solutions, one from adding the discriminant to -b and one from subtracting the discriminant from -b. If the square root is of zero, then it equals zero, and the solution is -b/2a. If the square root is of a negative number, then you have two imaginary solutions because you can't take the square root of a negative number and get a real number. One solution is from subtracting the discriminant from -b and dividing by 2a, and the other is from adding it to -b and dividing by 2a. The parabola on the left has a positive discriminant. The parabola in the middle has a discriminant of zero. The parabola on the right has a negative discriminant.
Use the discriminant to determine how many real number solutions the quadratic equation -4j to the second power plus 3j - 28 equals 0 has?
It has no real roots.
What does the discriminant have to be in order for the roots of a quadratic to be irrational?
The discriminant must be a positive number which is not a perfect square.
Why does the discriminant determine the number and type of the solutions for a quadratic equation?
A quadratic equation is wholly defined by its coefficients. The solutions or roots of the quadratic can, therefore, be determined by a function of these coefficients - and this function called the quadratic formula. Within this function, there is one part that specifically determines the number and types of solutions it is therefore called the discriminant: it discriminates between the different types of solutions.
What is the discriminant to determine how many real number solutions the quadratic equation -4j2 plus 3j-28 equals 0 has?
The discriminant is -439 and so there are no real solutions.
What is true of the discriminant when the two real number solutions to a quadratic equation are rational numbers?
The discriminant must be a perfect square or a square of a rational number.
What is a discriminant and how does help to solve equations?
In the quadratic formula, the discriminant is b2-4ac. If the discriminant is positive, the equation has two real solutions. If it equals zero, the equation has one real solution. If the discriminant is negative, it has two imaginary solutions. This is because you find the square root of the discriminant and add or subtract it from -b and divide the sum or difference by 2a. If the square root is of a positive number, then you get two different solutions, one from adding the discriminant to -b and one from subtracting the discriminant from -b. If the square root is of zero, then it equals zero, and the solution is -b/2a. If the square root is of a negative number, then you have two imaginary solutions because you can't take the square root of a negative number and get a real number. One solution is from subtracting the discriminant from -b and dividing by 2a, and the other is from adding it to -b and dividing by 2a. The parabola on the left has a positive discriminant. The parabola in the middle has a discriminant of zero. The parabola on the right has a negative discriminant.
Using the discriminant determine the number and type of solutions for this equation?
There are an indeterminate number of invisible solutions.
What is the expression b2-4ac under the radical sign in the quadratic formula?
6
How do you know how many solutions a quadratic equation will have?
A quadratic equation has the formAx2 + Bx + C = 0,where A, B, and C are numbers and x is a variable. Since the polynomial here has degree 2 (the highest exponent of x), it either has 0, 1, 2, or infinitely many solutions.The infinitely many solutions only happens when A, B, and C are all equal to zero. Otherwise, we can find the number of solutions by examining the discriminant, which in this case is the quantity B2 - 4AC. If the discriminant is negative, there are no (real) solutions. If the discriminant equals zero, we have what is called a "repeated root" and there is exactly one (real) solution. Otherwise, if the discriminant is positive, there are two distinct (real) solutions.
What is the value of the discriminant b2 and minus 4ac for the quadratic equation 0 and minus2x2 and minus 3x plus 8 and what does it mean about the number of real solutions the equation has?
If you mean 2x^2 -3x +8 = 0 then the discriminant works out as -55 which is less than 0 meaning that the equation has no real roots and so therefore no solutions are possible.
Use the discriminant to determine how many real number solutions the quadratic equation -4j to the second power plus 3j - 28 equals 0 has?
It has no real roots.
How do you recognize when an equation has no real solution or an infinite number of solutions?
It depends on the equation. Also, the domain must be such that is supports an infinite number of solutions. A quadratic equation, for example, has no real solution if its discriminant is negative. It cannot have an infinite number of solutions. Many trigonometric equations are periodic and consequently have an infinite number of solutions - provided the domain is also infinite. A function defined as follows: f(x) = 1 if x is real f(x) = 0 if x is not real has no real solutions but an infinite number of solutions in complex numbers.
How do you know if a quadratic equation can be factored?
The answer depends on what the factors will be. For example, every quadratic can be factored if you allow complex numbers. If not, then it helps to use the discriminant. If it is positive, there are two real factors or solutions. If that positive number is a perfect square, then the factors are rational numbers. If not, they are real but not rational (irrational). If the discriminant is 0, there is one real solution. Lastly, if it is negative, there are no real solutions.
What does the discriminant have to be in order for the roots of a quadratic to be irrational?
The discriminant must be a positive number which is not a perfect square.
