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Question

The equationx2+2(m-1)x+m+5=0 has an equal and real root. Find the value of m.


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Solution

x2+2(m-1)x+m+5=0 compare the given equation with ax2+bx+c=0

a=1,b=2(m-1),&c=m+5

For positive roots,b2-4ac=0

4(m-1)24(m+5)=04(m-1)2=4(m+5)m2-2m+1=m+5m2-3m-4=0(m-4)(m+1)=0m=4andm=-1.

Hence, the required value of m is 4,&-1.


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