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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 many soloutions does an inequality have?
Quite often, it has infinitely many solutions. For example: x > 5 Any number greater than 5 will work here. It need not even be a whole number. It is also possible for an equation involving inequalities to have one or no solution. For instance: x squared < 0 Has zero solutions (at least, in the set of real numbers).
How many real solutions does a quadratic function have when the value of its discriminant is seven?
If the discriminant is positive, as in this case, there are two real solutions.Also: * If the discriminant is zero, there is one real solution, considered to be a "double solution" because of the way polynomials are factored. * If the discriminant is negative, there are two complex solutions, which are complex and non-real.
How many real solutions are there to the equqtion 4x2 plus x-1 equals 0?
It has 2 real solutions because the discriminant is greater than zero.
How many real solutions are there for the equation x2 plus 3x plus 5 equals 0?
There are no real solutions because the discriminant of the quadratic equation is less than zero.
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 many soloutions does an inequality have?
Quite often, it has infinitely many solutions. For example: x > 5 Any number greater than 5 will work here. It need not even be a whole number. It is also possible for an equation involving inequalities to have one or no solution. For instance: x squared < 0 Has zero solutions (at least, in the set of real numbers).
Is a real number always sometimes or never a rational number?
Sometimes. The number '4' is real and rational. The number 'pi' is real but not rational.
How many solution will there be if the quadratic equation does not touch or cross the x-axis?
0 real solutions. There are other solutions in the complex planes (with i, the imaginary number), but there are no real solutions.
Is a real number always sometimes or never an irrational number?
sometimes
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 does all real number are solutions?
It is a statement without any particular meaning.
When are these kinds of numbers solutions to quadratic equations?
You need to be more specific. A quadratic equation will have 2 solutions. The 2 solutions can be equal (such as x² + 2x + 1 = 0, solution is -1 and -1). If one of the solutions is a real number, then the other solution will also be a real number. If one of the solutions is a complex number, then the other solution will also be a complex number. [a complex number has a real component and an imaginary component]In the equation: Ax² + Bx + C = 0. The term [B² - 4AC] will determine if the solution is a double-root, or if the answer is real or complex.if B² = 4AC, then a double-root (real).if B² > 4AC, then 2 real rootsif B² < 4AC, then the quadratic formula will produce a square root of a negative number, and the solution will be 2 complex numbers.If B = 0, then the numbers will be either pure imaginary or real, and negatives of each other [ example 2i and -2i are solutions to x² + 4 = 0]Example of 2 real and opposite sign: x² - 4 = 0; 2 and -2 are solutions.
Is a real number and rational number sometimes the same?
Yes, sometimes although a lot more often it is not.
How many real solutions can the quadratic formula give?
A quadratic equation can have either two real solutions or no real solutions.
Why does an inequality have 2 solutions?
An inequality, like an equation, can have a different number of solutions depending on the inequality and the domain.For example, x2< 0 has no solutions if the domain is the real numbers.x< 5 has only one solution ( = 4) if the domain consists of the squares of positive even numbers.x < 5 has infinitely many solutions if the domain is the rational numbers or real numbers.An inequality, like an equation, can have a different number of solutions depending on the inequality and the domain.For example, x2< 0 has no solutions if the domain is the real numbers.x< 5 has only one solution ( = 4) if the domain consists of the squares of positive even numbers.x < 5 has infinitely many solutions if the domain is the rational numbers or real numbers.An inequality, like an equation, can have a different number of solutions depending on the inequality and the domain.For example, x2< 0 has no solutions if the domain is the real numbers.x< 5 has only one solution ( = 4) if the domain consists of the squares of positive even numbers.x < 5 has infinitely many solutions if the domain is the rational numbers or real numbers.An inequality, like an equation, can have a different number of solutions depending on the inequality and the domain.For example, x2< 0 has no solutions if the domain is the real numbers.x< 5 has only one solution ( = 4) if the domain consists of the squares of positive even numbers.x < 5 has infinitely many solutions if the domain is the rational numbers or real numbers.
Is a real number sometimes a rational number?
Infinitely rarely, a real number is also a rational number. (There are an infinite number of rational numbers, but there are a "much bigger infinity" of real numbers.)
