Question

Select the correct answer from each drop-down menu.

Answer 1

Answer:

correct option for first blank is 5/4 and for second blank is $\frac{ 3i\sqrt{7}}{4}$

i.e m= $\frac{5}{4}\pm\frac{ 3i\sqrt{7}}{4}$

Step-by-step explanation:

The given equation

$m^2 - \frac {5m}{2} = \frac{-11}{2}$

and we have to find m= ______ ± ________

We can use quadratic formula to solve this question.

The above equation can be written as: $m^2 - \frac {5m}{2} + \frac{11}{2} = 0$

and the formula used will be:

$m= \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Putting values of a= 1, b= -5/2 and c= 11/2 and solving we get:$m=\frac{-\frac{-5}{2}\pm\sqrt{{(\frac{-5}{2})}^2-4(1)(\frac{11}{2})}}{2(1)}\\\\m=\frac{\frac{5}{2}\pm\sqrt{(\frac{25}{4})-22}}{2}\\m=\frac{\frac{5}{2}\pm\sqrt{(\frac{-63}{4})}}{2}\\m= \frac{\frac{5}{2}}{2}\pm\frac{\sqrt{(\frac{-63}{4})}}{2}\\m= \frac{5}{4}\pm\frac{\sqrt{-63}}{4}$

Since there is - sign inside the √ so $\sqrt{-1}$ is equal to i and we have to divide $\sqrt{63}$ into its multiples such that the square root of one multiple is whole no so,

$\sqrt{63}$  = $\sqrt{9}* \sqrt{7}$=$3* \sqrt{7}$

Putting value of $\sqrt{63}$ and $\sqrt{-1}$

the value of m= $\frac{5}{4}\pm\frac{ 3i\sqrt{7}}{4}$

so, correct option for first blank is 5/4 and for second blank is $\frac{ 3i\sqrt{7}}{4}$ .