Question

How do we determine the equation with the given roots?

Answer 1

`x^2-4=0`

Step-by-step explanation

The intercept (roots) form of a quadratic equation is:

`a(x-p)(x-q)=0`

where a = leading coefficient

p, q = roots of the equation

Hence, the quadratic equation whose roots are 2 and -2 and has a leading coefficient of 1 is:

`\begin{gathered} 1(x-2)(x-(-2))=0 \\ (x-2)(x+2)=0 \\ \Rightarrow x^2-2x+2x-4=0 \\ x^2-4=0 \end{gathered}`

That is the answer.