Write a quadratic equation in standard form with the given roots. 3/2, 1/4

The quadratic equation in standard form is  .

Explanation:

From Algebra, we remember that the order of the polynomial indicates the number of roots contained within. The factorized form of a second order polynomial (quadratic equation) is now introduced:

(1)

Where:

- Independent variable.

- Dependent variable.

, - Roots of the polynomial.

And the standard form of the quadratic equation:

(2)

Where , , are the coefficients of the polynomial.

Lastly, we proceed to perform algebraic operations until standard form is found:

1) , Given

2) By 1)/Definition of factorized form

3) Definition of subtraction

4) Distributive property

5) Distributive and commutative properties

6) Distributive and associative properties/

7)  /

8) Definition of substraction/Result