Question

Write the quadratic equation whose roots are

4 and −2, and whose leading coefficient is 3.
(Use the letter x to represent the variable.)

Answer 1

The quadratic equation
`y = ax^2 +bx+c` can be written in the form:

`y = a(x-p)(x-q)`
Where p and q are the roots of the equation.
Given p = 4, q = -2, a = 3, the quadratic will look like this:

`y = 3(x-4)(x+2)`
Finally, distribute and combine like terms to put it in standard form.

`y = 3(x^2 - 4x+2x -8) \\ \\ y = 3(x^2 -2x-8) \\ \\ y = 3x^2 -6x -24`