Question

Find the value of k for which the quadratic equation 3

3x^+2+k=0 has two equal roots.​

Answer 1

${\underline{\purple{\mathfrak{Correct \: question \: - }}}} \:$

• $\sf \: a \: quadratic \: equation \: \bold{ {3x}^{2} + kx + 3= 0} \ \: \: has \: two \: equal \: roots.$

${\underline{\purple{\mathfrak{We \: have \: to \: find \: - }}}}$

• $\sf \: the \: value \: of \: \bold{k}.$

${\underline{\purple{\mathfrak{As \: we \: know \: that \: -}}}}$

$\sf \: If \: a \: quadratic \: equation \: has \: two \: roots \: equal, \: then \: discriminant \: (D) = 0.$

$\boxed{\boxed{\bold\gray{\bigstar \: discriminant \: = b {}^{2} - 4ac }}}$

$\underline{\purple{\mathfrak{Here, \: we \: have \: - }}}$

• $\sf \: a \: = 3$
• $\sf \: b = k$
• $\sf c = 3$

$\underline\bold\purple{According \: to \: question \: - \: }$

$\sf\implies \: discriminant \: = {b}^{2} - 4ac \\ \\ \sf\implies \: 0 = {k}^{2} - (4 \times 3 \times 3) \\ \\ \sf\implies0 = {k}^{2} - 36 \\ \\ \sf\implies \: {k}^{2} = 36 \\ \\ \sf\implies \: k = \sqrt{36} \\ \\ \sf\implies \: k \: = \boxed{\bold\purple{6}}$

$\sf\therefore\underline{Hence, \: the \: value \: of \: k \: is \: \bold{6}.}$