Question

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

Answer 1

Answer:

The value of k is $k=\frac{15}{4}$  or  $k=3.75$

Step-by-step explanation:

Given : If $x=-\frac{1}{2}$ is a solution of the quadratic equation $3x^2+2kx+3=0$.

To find : The value of k ?

Solution :

To get the value of k substitute the value of x in the equation,

Equation $3x^2+2kx+3=0$

Put $x=-\frac{1}{2}$,

$3(-\frac{1}{2})^2+2k(-\frac{1}{2})+3=0$

$3(\frac{1}{4})-k+3=0$

$\frac{3}{4}-k+3=0$

$k=\frac{3}{4}+3$

$k=\frac{3+12}{4}$

$k=\frac{15}{4}$

$k=3.75$

Therefore, The value of k is $k=\frac{15}{4}$  or  $k=3.75$

Answer 2

Answer:

$Value\:of \: k = \frac{15}{4}$

Step-by-step explanation:

$Given \:x=\frac{-1}{2}\: is \:a \\solution \: of \:the\: quadratic\: equation\\3x^{2}+2kx+3=0$

$Substitute \:x=\frac{-1}{2}\:in \:the \\ equation ,\:we \:get$

$\implies 3\left(\frac{-1}{2}\right)^{2}+2k\left(\frac{-1}{2}\right)+3=0$

$\implies 3\left(\frac{1}{4}\right)-k+3=0$

$\implies \frac{3}{4}+3-k=0$

$\implies \frac{3+12}{4}-k =0$

$\implies \frac{15}{4}-k=0$

$\implies -k = -\frac{15}{4}$

$\implies k = \frac{15}{4}$

Therefore,

$Value\:of \: k = \frac{15}{4}$

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