How can you tell how many solutions an equation has without solving?

Correct answer: The coefficients are the numbers alongside the variables. The constants are the numbers alone with no variables. If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur.

How do you know if a quadratic equation has one solution?

The first way to tell if a quadratic has one solution is to look at the discriminant. If the discriminant is zero, then the quadratic equation has only one real solution. The discriminant is the expression b2 – 4ac under the radical in the quadratic formula.

How can you tell how many solutions a discriminant has?

It tells you the number of solutions to a quadratic equation. If the discriminant is greater than zero, there are two solutions. If the discriminant is less than zero, there are no solutions and if the discriminant is equal to zero, there is one solution.

How can you determine how many solutions a quadratic function has?

The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation.

1. A positive discriminant indicates that the quadratic has two distinct real number solutions.
2. A discriminant of zero indicates that the quadratic has a repeated real number solution.

How many solutions does quadratic equation have?

2 solutions
As we have seen, there can be 0, 1, or 2 solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b2 – 4ac), is positive, negative, or zero. This expression has a special name: the discriminant.

How do you determine the number of solutions?

Calculate the discriminant to determine the number and nature of the solutions of the following quadratic equation: y = x² − 2x + 1. In this quadratic equation,y = 1x² − 2x + 1. a = 1. b = − 2. c = 1.

Which equation has the solutions?

The answer is An equation sometimes has one solution. a linear (1st order) equation will have one solution. a quadratic (2nd order) equation will have two solutions. a cubic (3rd order) equation will have three solutions.

What does infinitely many solutions mean?

When an equation has infinitely many solutions, it means that if the variable was turned into a number, the equation would be correct or true, no matter which number or value is placed.