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  • Find the value of k for which the given quadratic equation has real and distinct roots and also find the roots. k x^2 +2x+1=0.

Find the value of k for which the given quadratic equation has real and distinct roots and also find the roots. k x^2 +2x+1=0.

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eginarrayl extGiven.\ kx^2+2x+1=0 ext, It roots are real and distinc.\ extAs we know, ax^2+bx+c=0 , x=fracleft(-b+sqrtb^2-4ac ight)2a\ extSo, roots of given equcation\ x=fracleft(-2+sqrt2^2-4k ight)2k\ extFor real roots, D>0 , \ 2^2-4k>0 \ Rightarrow k<1\ extSo, all values of k<1, extroots are real and distinct.endarray

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Deependra Verma

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