How many real solutions does a negative number have?
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 the formula for negative exponents?
A negative exponent takes us to the inverse of the number. In other words, a-n = 1/an and 5-3 becomes 1/53 = 1/125. This is how negative exponents change the numbers to fractions. Let us take another example to see how negative exponents change to fractions.
How do you get rid of negative exponents with variables?
A base that has a negative exponent can be changed to a fraction. The base and the exponent become the denominator, but the exponent loses its negative sign in the process. You then cap it all off with a 1 in the numerator.
What happens if you get a negative in quadratic formula?
This relationship is always true: If you get a negative value inside the square root, then there will be no real number solution, and therefore no x-intercepts. In other words, if the the discriminant (being the expression b2 − 4ac) has a value which is negative, then you won’t have any graphable zeroes.
Can real solutions be negative?
If the value of the discriminant is zero, there is one real solution for x, meaning the graph of the solution has one x-intercept. If a negative number is inside the square root, there are no x-intercepts. The solutions are not real numbers, but would have to be expressed as complex numbers.
How do you find all real solutions by factoring?
The Solve by Factoring process will require four major steps:
- Move all terms to one side of the equation, usually the left, using addition or subtraction.
- Factor the equation completely.
- Set each factor equal to zero, and solve.
- List each solution from Step 3 as a solution to the original equation.
Can a real solution be negative?
The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation. A positive discriminant indicates that the quadratic has two distinct real number solutions. A discriminant of zero indicates that the quadratic has a repeated real number solution.
Does absolute value apply negative exponents?
So that is the exponent rule, that is the rule for negative exponents and this is one way to think about it. Here’s another way to think think about it. Any negative number can be written as zero minus the absolute value of that number. For example, we could write -3 as 0- 3.
How many real solutions does a quadratic equation have if its discriminant is negative?
no real number
Because the discriminant is negative, the quadratic equation has no real number solutions, only two imaginary ones.
How do you determine the number of real solutions?
The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation.
- A positive discriminant indicates that the quadratic has two distinct real number solutions.
- A discriminant of zero indicates that the quadratic has a repeated real number solution.