Question

The roots of the equation x² +k(4x+k-1)+2=0 are equal, find the value of k.
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Answer 1

Answer:

x^2+k(4x+k-1)+2=0

x^2+4kx+k^2-k+2=0

=> a=1 ,b=4k, c=k^2-k+2

If roots are equal then D=0

=>b^2-4ac=0

=>(4k)^2-4×1×(k^2-k+2)=0

=>16k^2-4k^2+4k-8=0

=>12k^2+4k-8=0

=>3k^2+k-2=0

=>3k^2+3k-2k-2=0

=>3k(k+1)-2(k+1)=0

=>(k+1)(3k-2)=0

=>k=-1,2/3