Which equation has only one solution?
2 Answers By Expert Tutors
A quadratic equation only has one solution if the discriminant is zero.
How do you show that an equation has one real solution?
If there exists more than one real solution for f(x)=0 then f(a)=0=f(b)⟹a=b, and thus there is only one real solution to the equation, as desired.
What is an example of a real solution?
The number of solutions is determined by the discriminant. … If the discriminant is zero, then there is exactly one real solution. For example, in the quadratic equation x2 + 4x + 4 = 0, its discriminant is equals to. b2 − 4ac = (4)2 − 4(1)(4) = 0 and so the equation has exactly one real solution.
What quadratic equation has only one solution?
When The Coefficient of x2 Is Equal To 1 (a = 1)
If this is true, then the quadratic has one solution, which is x = -b / 2. For example, the quadratic equation x2 + 8x + 16 has one solution.
What does it mean if an equation has one real root?
Thus, a parabola has exactly one real root when the vertex of the parabola lies right on the x-axis. The simplest example of a quadratic function that has only one real root is, y = x2, where the real root is x = 0.
How do you find the real solution?
What is meant by real solution?
Real solution definition
In chemistry, a real solution is a homogeneous mixture of at least two chemical substances. A “real” solution differs from a colloidal solution (colloid).
What is a real solution in quadratic equation?
If the discriminant is greater than 0, the quadratic equation has 2 real solutions. If the discriminant is equal to 0, the quadratic equation has 1 real solution. If the discriminant is less than 0, the quadratic equation has 0 real solutions.
How many real solutions are there?
2 real solutions
It determines the number and the type of solutions that a quadratic equation has. If the discriminant is positive, there are 2 real solutions. If it is 0 , there is 1 real repeated solution. If the discriminant is negative, there are 2 complex solutions (but no real solutions).
What is no real solution?
A quadratic equation has no solution when the discriminant is negative. From an algebra standpoint, this means b2 < 4ac. Visually, this means the graph of the quadratic (a parabola) will never touch the x axis. Of course, a quadratic that has no real solution will still have complex solutions.
Is a real rational solution?
If the discriminant is a perfect square, then the solutions to the equation are not only real, but also rational. If the discriminant is positive but not a perfect square, then the solutions to the equation are real but irrational.
Is 0 a real solution?
zero, there is one real solution.
Which one is a quadratic equation?
A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b, and c being constants, or numerical coefficients, and x is an unknown variable.
Is a real root?
The terms solutions/zeros/roots are synonymous because they all represent where the graph of a polynomial intersects the x-axis. The roots that are found when the graph meets with the x-axis are called real roots; you can see them and deal with them as real numbers in the real world.
Are negative numbers real numbers?
Real numbers can be positive or negative, and include the number zero. They are called real numbers because they are not imaginary, which is a different system of numbers.
How do you find the real solutions of a polynomial equation?
Is 1 a real number?
The type of number we normally use, such as 1, 15.82, −0.1, 3/4, etc. Positive or negative, large or small, whole numbers or decimal numbers are all Real Numbers. They are called “Real Numbers” because they are not Imaginary Numbers.
Is Ia real number?
Essentially, an imaginary number is the square root of a negative number and does not have a tangible value. While it is not a real number — that is, it cannot be quantified on the number line — imaginary numbers are “real” in the sense that they exist and are used in math.