Question

If m^2-5/2m=-11/2,m=

Answer 1

Answer:  The required value of m is

$m=\dfrac{5+\sqrt{63}i}{4},~~~~~\dfrac{5-\sqrt{63}i}{4}.$

Step-by-step explanation:  We are given to find the vale of m if :

$m^2-\dfrac{5}{2}m=-\dfrac{11}{2}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

The given equation is a quadratic one, so we will be using the formula for the  solution of a quadratic equation $ax^2+bx+c=0,~a\neq 0$ as follows :

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}.$

From equation (i), we have

$m^2-\dfrac{5}{2}m=-\dfrac{11}{2}\\\\\\\Rightarrow 2m^2-5m+11=0\\\\\Rightarrow x=\dfrac{-(-5)\pm\sqrt{(-5)^2-4\times2\times11}}{2\times2}\\\\\\\Rightarrow x=\dfrac{5\pm\sqrt{25-88}}{4}\\\\\\\Rightarrow x=\dfrac{5\pm\sqrt{-63}}{4}\\\\\\\Rightarrow x=\dfrac{5\pm\sqrt{63}i}{4}.$

Thus, the required value of m is

$m=\dfrac{5+\sqrt{63}i}{4},~~~~~\dfrac{5-\sqrt{63}i}{4}.$

Answer 2

The answer is m = ( 5 ± 3i√7) / 4