Respuesta :

luisejr77

Answer: [tex]m=\frac{5}{4}\±\frac{3}{4}i\sqrt{7}[/tex]

Step-by-step explanation:

Use the Quadratic formula:

[tex]m=\frac{-b\±\sqrt{b^2}-4ac}{2a}[/tex]

Given the quadratic equation [tex]m^2-\frac{5}{2}m=-\frac{11}{2}[/tex]

Make it equal to zero:

[tex]m^2-\frac{5}{2}m+\frac{11}{2}=0[/tex]

You can see that :

[tex]a=1\\b=-\frac{5}{2}\\\\c=\frac{11}{2}[/tex]

Substitute values:

[tex]m=\frac{-(-\frac{5}{2})\±\sqrt{(-\frac{5}{2})^2-4(1)(\frac{11}{2})}}{2*1}\\\\m=\frac{\frac{5}{2}\±\sqrt{-\frac{63}{4}}}{2}\\\\m=\frac{\frac{5}{2}\±\frac{3}{2}i\sqrt{7}}{2}\\\\m=\frac{5}{4}\±\frac{3}{4}i\sqrt{7}[/tex]

(Remember that [tex]\sqrt{-1}=i[/tex])

alinakincsem

Answer:

[tex] m = \frac { 5 } { 4 } \pm\frac { 3 } { 4 } i \sqrt { 7 } [/tex]

Step-by-step explanation:

We are given the following equation and we are to solve it for m:

[tex] m ^ 2 - \frac { 5 } { 2 } m = - \frac { 1 1 } { 2 } [/tex]

We will solve this using the quadratic formula [tex]\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex].

Rearranging the equation to get:

[tex]m^2-\frac{5}{2}m+\frac{11}{2}=0[/tex]

Substituting the given values in the above formula to get:

[tex]m=\frac{-(-\frac{5}{2})\±\sqrt{(-\frac{5}{2})^2-4(1)(\frac{11}{2})}}{2\times1}\\\\m=\frac{\frac{5}{2}\±\sqrt{-\frac{63}{4}}}{2}[/tex]

We know that [tex]\sqrt{-1}=i[/tex].

[tex]m=\frac{\frac{5}{2}\±\frac{3}{2}i\sqrt{7}}{2}\\\\m=\frac{5}{4}\±\frac{3}{4}i\sqrt{7}[/tex]