Question

Find the value of k for which the quadratic equation 3x^2 +kx+3=0 has real and equal roots.

Answer 1

for roots equal and real

b^2 _ 4ac =0

so a=3,b=K and c=3

k^2 _ 4×3×3=0

k^2 =0+36

k=under root 36

k=6

Answer 2

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

$\green{\tt{\therefore{Value\:of\:k=\pm 6}}}$

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

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

• According to given question :

$\tt{ : \implies 3x^{2} +kx + 3= 0} \\ \\ \tt{\circ \: a = 3} \\ \\ \tt{\circ \: b = k}\\\\ \tt{\circ \:c = 3}\\ \\ \bold{Discriminant \: = 0} \\ \\ \tt{: \rightarrow \: D \implies {b}^{2} - 4ac = 0 } \\ \\ \tt{: \implies {b}^{2} - 4ac = 0} \\ \\ \text{Putting \: the \: given \: values} \\ \tt{: \implies (k)^{2} - 4\times3 \times 3= 0 } \\ \\ \tt{: \implies \: {k}^{2} -36 = 0 } \\ \\ \tt{ : \implies \: ({k}^{2} - 6^{2}) = 0 } \\\\ \tt{: \implies (k-6)(k+6)=0} \\ \\ \tt{: \implies k=6\:and\:-6} \\ \\ \green{\tt{: \implies k = \pm 6 }}$