Exercise 6 Page 914

We want to determine which of the given quadratic equations has the roots 12 and 13. To do so, we can write a quadratic equation in factored form using the given roots. Then we will rewrite it to be in standard form by multiplying the factors. rr Factored Form: & a(x- p)(x- q)=0 Standard Form: & ax^2+ bx+ c=0In the factored form, p and q are the roots of the equation. Since we are told that the roots are 12 and 13, we can partially write the factored form of our equation. a( x- 12 ) ( x- 13 )=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= 6. This is a common multiple of both denominators of the given roots and will allow us to eliminate the fractions when we distribute. Let's substitute this value and use the Distributive Property to obtain the standard form.

Note that we obtained the equation from option J. Therefore, J is the correct answer.