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What else can I help you with?
What is the expression b2-4ac under the radical sign in the quadratic formula?
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How do you find the discriminant and number of real solutions to a quadratic equation?
To find the discriminant of a quadratic equation in the form ax^2 + bx + c = 0, you use the formula Δ = b^2 - 4ac. The discriminant helps determine the nature of the roots: if Δ > 0, there are two distinct real roots; if Δ = 0, there is one real root (a repeated root); and if Δ < 0, there are no real roots (two complex conjugate roots). The number of real solutions is directly related to the discriminant's value.
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.
Explain how you an determine if the number is a solution of an equation?
Substitute the number in the equation. If the resulting statement is true the number is a solution to the equation.
Explain why the roots of a quadratic equation are imaginary if the value of the discriminant is less than 0?
The square of any real number is non-negative. So no real number can have a negative square. Consequently, a negative number cannot have a real square root. If the discriminant is less than zero, the quadratic equation requires the square root of that negative value, which cannot be real and so must be imaginary.
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.
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 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.
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 is the expression b2-4ac under the radical sign in the quadratic formula?
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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.
Can a graph be used to determine the number of solutions an equation has?
Yes.
Use the quadratic equation y equals x2 plus 3x plus 9 Calculate the discriminant to determine the number of real roots?
The discriminant is -27 and so there are no real roots.
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.
How do you determine the number of solutions of an equation?
the maximum number of solutions to an euation is equal to the highest power expressed in the equation. 2x^2=whatever will have 2 answers
How do you find the discriminant and number of real solutions to a quadratic equation?
To find the discriminant of a quadratic equation in the form ax^2 + bx + c = 0, you use the formula Δ = b^2 - 4ac. The discriminant helps determine the nature of the roots: if Δ > 0, there are two distinct real roots; if Δ = 0, there is one real root (a repeated root); and if Δ < 0, there are no real roots (two complex conjugate roots). The number of real solutions is directly related to the discriminant's value.
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.
