Question

k का मान ज्ञात कीजिए जिसके लिए बहुपद kx+x+kके sunyak barabar hun​

Answer 1

SOLUTION

TO DETERMINE

The value of k for which the below equation has equal roots

$\sf{k {x}^{2} + x + k = 0}$

EVALUATION

Here the given equation is

$\sf{k {x}^{2} + x + k = 0}$

Now it is given that the roots of the quadratic equation are equal

∴ Discriminant = 0

$\displaystyle \sf{ \implies \: {1}^{2} - 4 \times k \times k = 0 }$

$\displaystyle \sf{ \implies \: 1- 4 {k}^{2} = 0 }$

$\displaystyle \sf{ \implies \: 4 {k}^{2} = 1 }$

$\displaystyle \sf{ \implies \: {k}^{2} = \frac{1}{4} }$

$\displaystyle \sf{ \implies \: k = \pm \: \sqrt{ \frac{1}{4} } }$

$\displaystyle \sf{ \implies \: k = \pm \: \frac{1}{2} }$

FINAL ANSWER

Hence the required value

$\boxed{ \: \: \displaystyle \sf{ k = \pm \: \frac{1}{2} } \: \: }$

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