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

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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b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: