Question

If x = -3 is a solution of the quadratic equation 3x2

+ 2kx – 3 = 0, find the value of k.​

Answer 1

Given :

• The given quadratic equation is 3x²+2kx-3=0

• The value of x =-3

To Find :

• The value of k=?

Solution :

⇒The given quadratic equation is 3x²+2kx-3=0

⇒x=-3

According to the given conditions :

$\\ \blue\bigstar\large\green{\underline{\sf{Substitute \: the \: value \: of \: x \: in \: equation }}}$

$\ \\ \implies \sf \: 3 {x}^{2} + 2kx - 3 = 0 \\ \\ \\ \implies \sf \: 3 {( - 3)}^{2} + 2k( - 3) - 3 = 0 \\ \\ \\ \implies \sf \: 3 \times 9 - 6k - 3 = 0 \\ \\ \\ \implies \sf \: 27 - 6k - 3 = 0 \\ \\ \\ \implies \sf \: 27 - 3 - 6k = 0 \\ \\ \\ \implies \sf \: 24 - 6k = 0 \\ \\ \\ \implies \sf \: k = \frac{24}{6} \\ \\ \\ \implies \boxed{ \sf{k = 4}}$

⇒The value of k is 4

$\\ \large\green{\underline{\sf{Additional \: information :}}}$

•If the question ask to find the roots of the given quadratic equation we use formula method and determinant method.

$\\ \star\pink{\underline{\sf{Formula \: method}}}$

$\red \bigstar \boxed{ \sf{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} }}$

$\\ \star\pink{\underline{\sf{Determinant \: method}}}$

$\red \bigstar \boxed{ \sf{ \delta d = {b}^{2} - 4ac}}$

Answer 2

Step-by-step explanation:

Given :

•The given quadratic equation is 3x²+2kx-3=0

•The value of x =-3

To Find :

• The value of k=?

Solution :

⇒The given quadratic equation is 3x²+2kx-3=0

⇒x=-3

According to the given conditions :

\begin{gathered}\\ \blue\bigstar\large\green{\underline{\sf{Substitute \: the \: value \: of \: x \: in \: equation }}}\end{gathered}

★

Substitutethevalueofxinequation

\begin{gathered} \ \\ \implies \sf \: 3 {x}^{2} + 2kx - 3 = 0 \\ \\ \\ \implies \sf \: 3 {( - 3)}^{2} + 2k( - 3) - 3 = 0 \\ \\ \\ \implies \sf \: 3 \times 9 - 6k - 3 = 0 \\ \\ \\ \implies \sf \: 27 - 6k - 3 = 0 \\ \\ \\ \implies \sf \: 27 - 3 - 6k = 0 \\ \\ \\ \implies \sf \: 24 - 6k = 0 \\ \\ \\ \implies \sf \: k = \frac{24}{6} \\ \\ \\ \implies \boxed{ \sf{k = 4}}\end{gathered}

⟹3x

2

+2kx−3=0

⟹3(−3)

2

+2k(−3)−3=0

⟹3×9−6k−3=0

⟹27−6k−3=0

⟹27−3−6k=0

⟹24−6k=0

⟹k=

6

24

⟹

k=4

⇒The value of k is 4

\begin{gathered}\\ \large\green{\underline{\sf{Additional \: information :}}}\end{gathered}

Additionalinformation:

•If the question ask to find the roots of the given quadratic equation we use formula method and determinant method.

\begin{gathered}\\ \star\pink{\underline{\sf{Formula \: method}}}\end{gathered}

⋆

Formulamethod

\red \bigstar \boxed{ \sf{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} }}★

x=

2a

−b±

b

2

−4ac

\begin{gathered}\\ \star\pink{\underline{\sf{Determinant \: method}}}\end{gathered}

⋆

Determinantmethod

\red \bigstar \boxed{ \sf{ \delta d = {b}^{2} - 4ac}}★

δd=b

2

−4ac