求高人解数学问题.英文的!解得好的话加分!findvaluesofKintheequationX^2+(K+1)X+((K+1)/4)=0IF:a)rootsareequalinmagnitudebutoppositeinsignb)rootsareequalc)onerootis1d)rootsarereciprocalsofoneanother

Question

求高人解数学问题.英文的!解得好的话加分!
find values of K in the equation

X^2+(K+1)X+((K+1)/4)=0
IF:
a)roots are equal in magnitude but opposite in sign
b)roots are equal
c)one root is 1
d)roots are reciprocals of one another
e)roots are real
我知道问题问得是什么，，，我要的是答案。。。还有步骤。。越详细越好，，，最好可以解释一下你是怎么做的，，，从何入手，，，

Answer 1

a)两根大小相等,方向相反,
设两根为X1和X2,则由韦达定理有
X1+X2=-(K+1)/2,故-(K+1)/2=0,K=-1
b)两根相等,
则△=(K+1)^2-(K+1)=0得K=0或1
c)一根为1,
直接将1代入得1+（K+1)+(K+1)/4=0,解出K=-9/5
d)两根互为相反数,意思和a)一样
e)根为实数,
即△=(K+1)^2-(K+1)≥0,解得K≥0或K≤-1