Answer:
C. -0.5, -1.5
Step-by-step explanation:
Given equation
[tex]4d^2+8d+3=0[/tex]
To solve for [tex]d[/tex]
As the above equation is of 2nd degree, so its a quadratic equation. We can solve is by using quadratic formula.
For a quadratic equation [tex]ax^2+bx+c=0[/tex]
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
So, for [tex]4d^2+8d+3=0[/tex]
[tex]d=\frac{-8\pm\sqrt{8^2-4(4)(3)}}{2(4)}[/tex]
[tex]d=\frac{-8\pm\sqrt{64-48}}{8}[/tex]
[tex]d=\frac{-8\pm\sqrt{16}}{8}[/tex]
[tex]d=\frac{-8\pm4}{8}[/tex]
So [tex]d=\frac{-8+4}{8}[/tex] and [tex]d=\frac{-8-4}{8}[/tex]
[tex]d=-\frac{1}{2}[/tex] and [tex]d=-\frac{3}{2}[/tex]
Or [tex]d=-0.5[/tex] and [tex]d=-1.5[/tex]
∴ [tex]d= -0.5, -1.5[/tex]
