Exercise 82 Page 176

Recall that you can solve a quadratic expression by factoring and using the Zero Product Property. We can do the inverse process to find a quadratic expression with the solutions that we want. We start with the product of two binomials of the form (x-c)(x-d)=0. Here c and d are real numbers. (x-c)(x-d)=0 Zero Product Property a* b = 0 ⇔ a =0 or b=0 x-c =0 1.5cm x-d=0 or x=c 2.1cm x=dWe can see that the product (x-c)(x-d) will be zero when x=c or x=d. We can pick any values for c and d and multiply the binomials to find the quadratic equation in standard form. Let's try with c=1 and d=2.

Now we can do the same thing, but this time consider opposite signs to see if something changes. We will then use c=-1 and d=-2

As can see, the sign of the linear term changed. In general, changing the signs of both integers we choose as solutions will only affect the linear term. However, the way it will be affected will depend on the values and signs of the integers chosen.