,

and are the two real distinct solutions for the quadratic equation, which means that and are the factors of the quadratic equation.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify each term.

Multiply by .

Combine and .

Move to the left of .

Multiply .

Combine and .

Multiply by .

Move the negative in front of the fraction.

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Combine the numerators over the common denominator.

Move to the left of .

Multiply by .

Subtract from .

Factor by grouping.

For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .

Factor out of .

Rewrite as plus

Apply the distributive property.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

Factor out the greatest common factor (GCF) from each group.

Factor the polynomial by factoring out the greatest common factor, .

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify each term.

Multiply by by adding the exponents.

Move .

Multiply by .

Multiply by .

Multiply by .

Add and .

Split the fraction into two fractions.

Split the fraction into two fractions.

Cancel the common factor.

Divide by .

Move the negative in front of the fraction.

Move the negative in front of the fraction.

The standard quadratic equation using the given set of solutions is .

Find the Quadratic Equation 5 , -19/4