One of the roots of the equation 4x2+bx+c=0 is 0.5. the other is equal toc. find the value of b andc.

Let's Go:

[tex]4x^2 + bx + c = 0 \\\ 4.(0,5)^2 + b.(0,5) + c = 0 \\\ 1 + 0,5b + c = 0 \\\ 0,5b + c = - 1 \\\\\ x' + x'' = \frac{-b}{a} \\\\ 0,5 + c = \frac{-b}{4} \\\\ 4(0,5 + c) = - b \\ b = - c - 2[/tex]

Changing b for - c - 2 at 0,5b + c = - 1:

[tex]0,5.(- c - 2) + c = - 1 \\\ - 0,5c - 1 + c = - 1 \\\ - 0,5c + c = 0 \\\ 0,5c = 0 \\\ c = 0[/tex]

Changing c for 0 in b = - c - 2:

[tex]b = 0 - 2 \\ b = - 2[/tex]

So, the equation is:
[tex]4x^2 - 2x = 0[/tex]
b = - 2; c = 0
The roots are 0 and 0,5

I hope I helped you. Sorry for the grammaticals error.