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[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.
raphealnwobi

The value of b = -3 and c = 0.5

A polynomial is an expression involving the operations of addition, subtraction, multiplication of variables.

Given that 0.5 is a root of 4x² + bx + c=0, hence:

4(0.5)² + b(0.5) + c = 0

1 + 0.5b + c = 0

0.5b + c = -1    (1)

Also the other root is c, hence:

4(c)² + b(c) + c = 0

4c² + bc + c = 0

4c + b + 1 = 0

4c + b = -1      (2)

Solving equation 1 and 2 simultaneously gives:

b = -3, c = 0.5

The equation is:

4x² - 3x + 0.5 = 0

Therefore the value of b = -3 and c = 0.5.

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