Question

# Nick and Dick were trying to solve the equation 3x2+8x+4=0 by the method of completion of squares. While trying to complete the squares, in one of the steps, Dick subtracted (76)2 whereas Nick subtracted (43)2 and both of them calculated the roots. Their teacher looked at the roots and told them that Nick’s roots are the additive inverses of Dick’s roots. True False

Solution

## The correct option is B False In the first step in the completion of squares, the entire equation is divided by 3, ⇒x2+8x3+43=0 ⇒x2+2(x)43+(43)2+43−(43)2=0 Here in this step Nick and Dick parted ways. Both of them added (43)2 Nick was on the right track by subtracting (43)2, but Dick subtracted (76)2 and his roots were altered. Nick's ProcessDick's Processx2+2(x)(43)+(43)2+43−(43)2=0x2+2(x)(43)+(43)2+43−(76)2=0       ⇒(x+43)2−49=0⇒(x+43)2−136=0⇒(x+43)2=49⇒(x+43)2=136⇒(x+43)2=±23⇒(x+43)2=±16⇒x=23−43,x=−23−43⇒x=16−43,x=−16−43⇒x=−23,−2⇒x=−76,−96 After finding the roots, it is clear that the roots are not the additive inverses of each other.

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