Question

Find the values of k for which the quadratic equation 9x2 – 3kx + k = 0
has equal roots.
answer is given - k is equal to 1​

Answer 1

Step-by-step explanation:

hi guys this is your answer

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Value\:of\:k=0\:and\:4}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{ \underline \bold{Given : }} \\ \tt{ : \implies 9x^{2} -3kx + k = 0 }\\ \\ \red{ \underline \bold{To \: Find : }} \\ \tt{: \implies value \: of \: k = ?}$

• According to given question :

$\tt{ : \implies 9x^{2} +3kx + k= 0} \\ \\ \tt{\circ \: a = 9} \\ \\ \tt{\circ \: b =- 3k}\\\\ \tt{\circ \:c = k}\\ \\ \bold{Discriminant \: = 0} \\ \\ \tt{: \rightarrow \: D \implies {b}^{2} - 4ac = 0 } \\ \\ \tt{: \implies {b}^{2} - 4ac = 0} \\ \\ \text{Putting \: the \: given \: values} \\ \tt{: \implies (-3k)^{2} - 4\times9\times k= 0 } \\ \\ \tt{: \implies \: 9{k}^{2} -36k = 0 } \\ \\ \tt{ : \implies \: 9({k}^{2} - 4k) = 0 } \\\\ \tt{: \implies k(k-4)=0} \\ \\ \tt{: \implies k= 0\:and\:4} \\ \\ \green{\tt{\therefore k =0\:and\:4}}$