Can a discriminant be imaginary?
Can a discriminant be imaginary?
The discriminant of a quadratic function can only be imaginary if at least some of the coefficients of the quadratic are imaginary.
How do you find the discriminant and number of real solutions?
The discriminant is the formula b squared minus 4ac remembering that a, b and c are the coefficients of your quadratic in standard form. It tells you the number of solutions to a quadratic equation. If the discriminant is greater than zero, there are two solutions.
What are the imaginary solutions?
The imaginary unit or unit imaginary number (i) is a solution to the quadratic equation x2 + 1 = 0. Although there is no real number with this property, i can be used to extend the real numbers to what are called complex numbers, using addition and multiplication.
What are real and complex solutions?
The expression b2 − 4ac is called the discriminant, and can be used to determine whether the solutions are real, repeated, or complex: 1) If the discriminant is less than zero, the equation has two complex solution(s). 2) If the discriminant is equal to zero, the equation has one repeated real solution(s).
What is a complex solution?
If the discriminant equals 0, then the equation has one real solution, a double root. If the discriminant is less than 0, then the equation has two complex solutions. If the discriminant is greater than 0, then the equation has two real solutions.
What is the formula of discriminant?
The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.
What is the difference between real and complex solutions?
A real number can be a rational and irrational number and can have any value on the number line. A complex number exists in the form a + ib where i is used for denoting the imaginary part and a and b denote the real numbers.
What does real solutions mean in math?
A real solution in algebra is simply a solution to an equation that is a real number.
How do you know if the discriminant is real or imaginary?
If the solution is a real number or an imaginary number. If the solution is rational or if it is irrational . If the solution is one unique number or two different numbers. If the discriminant is a positive number, then there are 2 real solutions.
What information does the discriminant tell us about the equation?
The discriminant tells us the following information about a quadratic equation: If the solution is a real number or an imaginary number. If the solution is rational or if it is irrational. If the solution is one unique number or two different numbers.
What does it mean when the discriminant is zero?
When discriminant is zero, it shows that there are repeated real number solution to the quadratic; For a negative discriminant, neither of the solutions amount to real numbers; For a positive discriminant, there are two distinct real number solutions to the quadratic equation.
How do you find the number of rational solutions to discriminant?
Since the discriminant is positive and a perfect square, we have two real solutions that are rational. Calculate the discriminant to determine the nature and number of solutions: y = x² + 4x − 5 . In this quadratic equation, y = x² + 4x − 5.
