Table of Contents
- 1 What is the condition for infinite solution?
- 2 How can a quadratic have infinite solutions?
- 3 What is a one solution equation?
- 4 What is the condition for both roots of a quadratic equation to infinity?
- 5 How do you make a quadratic equation Infinity?
- 6 What are the zeros of a quadratic equation called?
What is the condition for infinite solution?
Conditions for Infinite Solution If the two lines have the same y-intercept and the slope, they are actually in the same exact line. In other words, when the two lines are the same line, then the system should have infinite solutions.
How can a quadratic have infinite solutions?
Systems of Two Quadratic Equations
| One Solution | No Solutions |
|---|---|
| Two Solutions | Infinite Solutions |
| Two quadratic equations that overlap but have different equations have two solutions. | If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations. |
Can a quadratic equation have infinite roots?
(b) Both the roots at infinity: When both roots of the equation are infinity, then the co-efficient of x2 and co-efficient of x both must tend to zero and c must not be equal to zero.
How do you know if a quadratic equation has one two or no solution?
The discriminant is the expression b2 – 4ac, which is defined for any quadratic equation ax2 + bx + c = 0. If you get 0, the quadratic will have exactly one solution, a double root. If you get a negative number, the quadratic will have no real solutions, just two imaginary ones.
What is a one solution equation?
If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions.
What is the condition for both roots of a quadratic equation to infinity?
ax²+bx+c=0 a≠0, has roots of infinity if b=0,c=∞.
What is the condition for no solution in quadratic equation?
Answer: for any quadratic equation or no real roots or no solution you need to satisfy the equation that is b² – 4ac < 0.
What does it mean when a quadratic only has one solution?
A quadratic equation has one solution when the discriminant is zero. From an algebra standpoint, this means b2 = 4ac.
How do you make a quadratic equation Infinity?
In the quadratic formula, the only way to make it infinity would be if a = 0. Then the denominator would be zero, and hence the whole equation would be “infinity.” But if a = 0, then the equation is no longer quadratic, it is linear, right? For example, is the same as . That is just a line, it is linear, not quadratic.
What are the zeros of a quadratic equation called?
These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation. The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics.
When does a quadratic equation become an identity?
A quadratic equation becomes an identity (a, b, c = 0) if the equation is satisfied by more than two numbers i.e. having more than two roots or solutions either real or complex.
How do you know if an equation is a quadratic equation?
Using the quadratic formula is often the most convenient way. If f (x) is a quadratic polynomial, then f (x) = 0 is called a quadratic equation.