Question

How do you write a quadratic equation with -6 and 3/4 as its roots? How do you write the equation in the form `ax^2+ bx+ c =0`, where a, b, and c are integers?

Answer 1

`4x^2+21x-18=0`

Explanation:

Sum of Root (SOR) `= -6+3/4 = -21/4`
Product of Root (POR) `=-6*3/4=-18/4`

General form for Quadratic Equation is `x^2-SORx+POR =0`
Therefore,
`x^2-(-21/4)x+(-18/4)=0`

`x^2+21/4x-18/4=0`

multiply by 4,

`4x^2+21x-18=0`