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Fill in the blanks to make a quadratic whose roots are $1$ and $-1.$
x^2 + ___ x + ___

 Jun 26, 2024

Best Answer 

 #1
avatar+1230 
+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! :)

 Jun 26, 2024
 #1
avatar+1230 
+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

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