Fill in the blanks to make a quadratic whose roots are $1$ and $-1.$

x^2 + ___ x + ___

gnistory Jun 26, 2024

#1**+1 **

Let's first note that the quadratic with roots 1 and -1 can be written in the form of

\((x-1)(x+1)=0\)

This is in the form of what we call factored form. Now, expanding this, we have

\(x(x+1) - 1(x+1)\)

Distributing the values in, we have

\(x^2+x-x-1\)

\(x^2-1\)

Thus, we have that the first blank is 0 and the second blank is -1.

Thanks! :)

NotThatSmart Jun 26, 2024

#1**+1 **

Best Answer

Let's first note that the quadratic with roots 1 and -1 can be written in the form of

\((x-1)(x+1)=0\)

This is in the form of what we call factored form. Now, expanding this, we have

\(x(x+1) - 1(x+1)\)

Distributing the values in, we have

\(x^2+x-x-1\)

\(x^2-1\)

Thus, we have that the first blank is 0 and the second blank is -1.

Thanks! :)

NotThatSmart Jun 26, 2024