c If a quadratic equation has two distinct roots that are additive opposites, then the roots add up to 0.
A
aExample Equation: x^2-4x+4=0
B
bExample Equation: 2x^2-7x+3=0
C
cExample Equation: x^2-16=0
Practice makes perfect
a A double root occurs when the quadratic equation is a perfect square trinomial. Let x=2 be the double root of our quadratic equation. With this, we can write the equation as shown below.
(x-2)(x-2)=0 ⇔ (x-2)^2=0
Now, to write the above equation in standard form, we can simplify the left-hand side.
c If a quadratic equation has two distinct integer roots that are additive opposites, then they add up to 0. Let's assume x=4 and x=-4 are the roots of the quadratic equation. From here, we can write the quadratic equation as follows.
(x-4)(x+4)=0
Now, we will apply the Distributive Property to simplify the left-hand side.
