Given:
The quadratic equation is:
[tex]10m^2-7m+3=0[/tex]
To find:
The solutions for the given equation by using the quadratic formula.
Solution:
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then the quadratic formula is:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
We have,
[tex]10m^2-7m+3=0[/tex]
Here, [tex]a=10,b=-7,c=3[/tex]. Using the quadratic formula, we get
[tex]m=\dfrac{-(-7)\pm \sqrt{(-7)^2-4(10)(3)}}{2(10)}[/tex]
[tex]m=\dfrac{7\pm \sqrt{49-120}}{20}[/tex]
[tex]m=\dfrac{7\pm \sqrt{-71}}{20}[/tex]
[tex]m=\dfrac{7\pm i\sqrt{71}}{20}[/tex] [tex][\because \sqrt{-a}=i\sqrt{a},a>0][/tex]
Therefore, the solution set of the given equation is [tex]\left\{\dfrac{7- i\sqrt{71}}{20},\dfrac{7+ i\sqrt{71}}{20}\right\}[/tex]. Hence, the correct option is D.
