Write the quadratic equation whose roots are - 2 and 1, and whose leading coefficient is 4.

Answer: the equation is

4x^2 + 4x - 12

Step-by-step explanation:

A quadratic equation is an equation in which the highest power of the unknown is 2.

The general form of a quadratic equation is expressed as

ax^2 + bx + c

Where

a is the leading coefficient

c is a constant

Assuming we want to write the quadratic equation in x, from the information given, the roots which are given are - 2 and 1 and the leading coefficient is 4.

Therefore, the linear factors of the quadratic equation will be (x+2) and (x-1)

the equation becomes

(x+2) (x-1)

= x^2 - x + 2x - 3

= x^2 + x - 3

Given a leading coefficient of 4, we will multiply the quadratic expression by 4. It becomes

4 (x^2 + x - 3)

= 4x^2 + 4x - 12