Exercise 3 Page 174

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 - 23 and 52, we can partially write the factored form of our equation. a( x-( - 2/3 ) ) ( x-5/2 )=0 ⇕ a( x+ 2/3 ) ( x-5/2 )=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. 6( x+ 2/3 ) ( x-5/2 )=0 Finally, let's use the Distributive Property to obtain the standard form.

Please note that this is just one example of a quadratic function that satisfies the given requirements.