Question

Write the quadratic equation whose roots are 1 and -1 whose coefficient is 2. (Use the letter x to represent the variable)

Answer 1

so that our equation has roots in 1 and -1 we are going to express the polynomial in the factored form

so

`y=a(x-b)(x-c)`

where a is the coefficient, b and c the roots

so replacing

`\begin{gathered} y=2(x-(-1))(x-(1)) \\ \\ y=2(x+1)(x-1) \end{gathered}`

then solve the multiplication

`\begin{gathered} y=2((x* x)+(x*-1)+(1* x)+(1*-1)) \\ y=2(x^2-x+x-1) \\ y=2x^2-2 \end{gathered}`