Question

if x=-1/2 is a solution of the 3x square + 2kx -3 =0 then the value of x is​

Answer 1

Question :

If x = -1/2 is a solution of the 3x² + 2kx - 3 = 0 then find value of k .

Solution:

$\tt{Equation \: is \: 3x^2 \: + \: 2kx \: - \: 3 \: = \: 0}$

$\rm{Substitute \: x \: = \: \dfrac{-1}{2} \: in \: Equation}$

$\sf{3( \dfrac{ - 1}{2} )^{2} \: + \: 2( \dfrac{ - 1}{2}k) \: - \: 3 \: = \: 0} \\ \\ \rightarrow \sf{3( \frac{1}{4}) \: + \: ( \dfrac{ - \cancel{ 2}}{ \cancel{2}}k ) \: - \: 3 \: = \: 0 } \\ \\ \rightarrow \sf{ \dfrac{3}{4} \: - \: 1k \: - \: 3 \: = \: 0} \\ \\ \rm{\gray{Take \: L.C.M}} \\ \\\rightarrow \sf{ \dfrac{3 \: - \: 4k \: - \: 12}{4} \: = \: 0} \\ \\ \rm {\gray{[ \because \: 0 \: \times \: (Any \: Number) \: = \: 0] }} \\ \\\rightarrow\sf{3 \: - \: 4k \: - 12 \: = \: 0} \\ \\ \sf{ \rightarrow - 4k \: - \: 9 \: = \: 0} \\ \\ \rightarrow \sf{ - 4k \: = \: 9} \\ \\ \rightarrow \sf{k \: = \: \frac{ - 9}{4} }$

$\Large{\boxed{\tt{\gray{Answer \: : \: \dfrac{-9}{4}}}}}$

Answer 2

Question

If x = - 1/2 is a solution of the equation 3x² + 2Kx - 3 = 0,then the value of K is :

Solution

Given Equation,

$\large{ \tt{3x {}^{2} + 2kx - 3 = 0}}$

ATQ,

$\boxed{ \boxed{ \tt{x = - \frac{1}{2} }}}$

Since,

- 1/2 is a solution of the given equation,on substituting back the equation would given zero as the result

Implies,

$\implies \: \tt{3( - \dfrac{1}{2}) {}^{2} - 2 \dfrac{K}{2} - 3 = 0 } \\ \\ \implies \ \tt{ \frac{3}{4} - K = 3} \\ \\ \implies \: \tt{K = \frac{3}{4} - 3 } \\ \\ \large{ \implies \: \boxed{ \boxed{ \tt{K = - \frac{9}{4} }}}}$

For K = -9/4,x = -1/2 is a root of the given equation