Question

if the roots of quadratic eq x^2+6x+k=0 are equal,then the value of k is​

Answer 1

$\boxed{ \underline{ \underline{\footnotesize\tt{ Solution:- }}}} \: \bigstar$

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$\footnotesize\tt{a = 1}$

$\footnotesize\tt{b= 6}$

$\footnotesize\tt{c= k}$

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$\boxed{ \underline{ \underline{\footnotesize\tt{ Given:-}}}} \: \bigstar$

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$\footnotesize\tt{D = 0}$

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$\boxed{ \underline{ \underline{\footnotesize\tt{ By \: D \: Method : - }}}} \: \bigstar$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\footnotesize\tt{ {b}^{2} - 4ac = 0 }$

$\footnotesize\tt{ {6}^{2} - 4 \times 1 \times k= 0 }$

$\footnotesize\tt{ 36 - 4 k= 0 }$

$\footnotesize\tt{ - 4 k= 0 - 36 }$

$\footnotesize\tt{ - 4 k= - 36 }$

$\footnotesize\tt{ k \: = \: } \tt{ \frac{ - 36}{ - 4} }$

$\footnotesize\tt{ k \: = \: } \tt{ \cancel\frac{ - 36}{ - 4} }$

$\boxed{ \underline{ \underline{\footnotesize\tt{ k \: = \:9 \: }}}} \: \bigstar$

Answer 2

Complete step-by-step answer:

Given that the quadratic equation has real and equal roots. If the discriminant of the quadratic expression is equal to zero, then the quadratic expression has equal real and equal roots. Hence the value of $k$ is $\dfrac{9}{2}$.

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