The discriminant tells you how many solutions there are to quadratic equation or how many x intercepts there are for a parabola. It tells you the number of solutions to a quadratic equation.

The procedure to use the discriminant calculator is as follows:

1. Step 1: Enter the coefficient values such as “a”, “b” and “c” in the given input fields.
2. Step 2: Now click the button “Solve” to get the output.
3. Step 3: The discriminant value will be displayed in the output field.
4. Discriminant, D = b2 – 4ac.

The discriminant is the expression b2 – 4ac, which is defined for any quadratic equation ax2 + bx + c = 0. Based upon the sign of the expression, you can determine how many real number solutions the quadratic equation has.

Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.

The four main types of factoring are the Greatest common factor (GCF), the Grouping method, the difference in two squares, and the sum or difference in cubes.

To factor a trinomial with two variables, the following steps are applied:

1. Multiply the leading coefficient by the last number.
2. Find the sum of two numbers that add to the middle number.
3. Split the middle term and group in twos by removing the GCF from each group.
4. Now, write in factored form.

To remove a common factor and rewrite a polynomial as the product of a monomial and another polynomial: Find the greatest common factor which is a whole number (no variables). Divide all terms of the polynomial by that factor, and put the result in parentheses. Write the factor outside the parentheses.

Common monomial factors, factoring special products and factoring polynomials

• or 9 59 2=9 5-2=9 3
• or x 7 x 2= x 7-2= x 5
• y 3 y 3= =11=1.
• or y 3 y 3= y 3-3= y 0=1.

A common monomial factor is a monomial that is a common factor to all of the terms of a polynomial.

Here’s how to find the GCF of a set of numbers using prime factorization:

1. List the prime factors of each number.
2. Circle every common prime factor — that is, every prime factor that’s a factor of every number in the set.
3. Multiply all the circled numbers. The result is the GCF.

Greatest common factors in monomials Simply write the complete factorization of each monomial and find the common factors. The product of all the common factors will be the GCF.

12

We found the factors and prime factorization of 45 and 36. The biggest common factor number is the GCF number. So the greatest common factor 45 and 36 is 9.

Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30. 3.

15

7

We found the factors and prime factorization of 12 and 27. The biggest common factor number is the GCF number. So the greatest common factor 12 and 27 is 3.

A Positive Discriminant If the discriminant is positive, this means that you have a positive number under the square root in the quadratic formula. The roots/zeros/solutions are the the values for x that make the equation equal to 0. On a graph, this will be where the parabola crosses the x-axis.

If the discriminant is negative, that means there is a negative number under the square root in the quadratic formula. You may have learned in the past that you “can’t take the square root of a negative number.” The truth is that you can take the square root of a negative number, but the answer is not real.

2

That’s negative, so there are two complex roots for this equation.

When discriminant is equal to zero, the roots are equal and real.

The fundamental theorem of algebra says that every polynomial function has at least one root in the complex number system. The highest degree of a polynomial gives you the highest possible number of distinct complex roots for the polynomial.

Explanation: To find the degree of the polynomial, add up the exponents of each term and select the highest sum. The degree is therefore 6.