+0  
 
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avatar+826 

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

 Jul 18, 2024
 #1
avatar+129852 
+1

(x + 1) ( x -1)   =  x^2 + 0x - 1

 

cool cool cool

 Jul 18, 2024
 #2
avatar+42 
+2

\(\text{By Vieta's formulae the sum of roots is -b/a, } \text{and the product is c/a}\)

if they are in an quadratic ax^2 + bx + c = 0

WE KNOW A = 1 :)

Therefore, the sum of the roots is -b and the product is c

The roots are 1 and -1, so the sum is 0 and the product is -1

Given that -b = 0 and c = -1, or b = 0 and c = 1, plug the values back into the equation x^2 + bx + c = 0 to get your final answer

 

blush 

Please like if this answer was correct. Thank you.

 Jul 18, 2024

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