Answer:
The value of k is -4.
Step-by-step explanation:
In order to find the value of k, you have to substitite x = -1/2 into the equation :
[tex]2 {x}^{2} - 7x + k = 0[/tex]
[tex]let \: x = - \frac{1}{2} [/tex]
[tex]2 {( - \frac{1}{2} )}^{2} - 7( - \frac{1}{2} ) + k = 0[/tex]
[tex]2( \frac{1}{4} ) + \frac{7}{2} + k = 0[/tex]
[tex] \frac{1}{2} + \frac{7}{2} + k = 0[/tex]
[tex]4 + k = 0[/tex]
[tex]k = - 4[/tex]
