1.

यदि व्यंजक `x^(2)+x+1,(x+1/2)^(2)+q^(2)`, के रूप में लिखा गया है तो `q` का संभावित मान क्या होगा?A. `+-1/3`B. `+-(sqrt(3))/2`C. `+-2/(sqrt(3))`D. `+-(1/2)`

Answer» Correct Answer - B
`x^(3)+x+1=0`………………i
`(x+1/2)^(2)+q^(2)=0`
`implies x^(2)+1/4+2xx1/2xx x+q^(2)`
`=x^(2)+x+(q^(2)+1/4)=0`…………….ii
Comparing constnat term of equation i and ii
`:. q^(2)+1/4=1`
`=q^(2)=1-1/4=3/4`
`q=+-sqrt(3/4)=+-(sqrt(3))/2`


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