We can write a quadratic equation in factored form using the given roots. Then we will change it to standard form by multiplying the factors.
Factored Form:& a(x-p)(x-q)=0
Standard Form:& ax^2+bx+c=0
In the factored form, p and q are the roots of the equation. Since we are told the roots are - 47 and 38, we can partially write the factored form of our equation.
a( x-( - 4/7 ) ) ( x-3/8 )=0
⇕
a( x+ 4/7 ) ( x-3/8 )=0
Since a does not have any effect on the roots, we can choose any value. For simplicity and in order to have integer coefficients, we will let a=56. This is a common multiple of both denominators of the given roots and will allow us to eliminate the fractions when we distribute.
56( x+ 4/7 ) ( x-3/8 )=0
Finally, let's use the Distributive Property to obtain the standard form.
