Answer:
correct option for first blank is 5/4 and for second blank is [tex]\frac{ 3i\sqrt{7}}{4}[/tex]
i.e m= [tex]\frac{5}{4}\pm\frac{ 3i\sqrt{7}}{4}[/tex]
Step-by-step explanation:
The given equation
[tex]m^2 - \frac {5m}{2} = \frac{-11}{2}[/tex]
and we have to find m= ______ ± ________
We can use quadratic formula to solve this question.
The above equation can be written as: [tex]m^2 - \frac {5m}{2} + \frac{11}{2} = 0[/tex]
and the formula used will be:
[tex]m= \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Putting values of a= 1, b= -5/2 and c= 11/2 and solving we get:[tex]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}[/tex]
Since there is - sign inside the √ so [tex]\sqrt{-1}[/tex] is equal to i and we have to divide [tex]\sqrt{63}[/tex] into its multiples such that the square root of one multiple is whole no so,
[tex]\sqrt{63}[/tex] = [tex]\sqrt{9}* \sqrt{7}[/tex]=[tex]3* \sqrt{7}[/tex]
Putting value of [tex]\sqrt{63}[/tex] and [tex]\sqrt{-1}[/tex]
the value of m= [tex]\frac{5}{4}\pm\frac{ 3i\sqrt{7}}{4}[/tex]
so, correct option for first blank is 5/4 and for second blank is [tex]\frac{ 3i\sqrt{7}}{4}[/tex] .
