Question

One root of the equation 4x^2+bx+c=0 is 0.5. The other is equal to c. Find the values of b and c.

Answer 1

Answer: -2 and 0 in order

Explanation:

If an equation has a root, then putting the root into the equation will give you zero.

4 ×
`0.5^(2)` + b × 0.5 + c = 0

1 +
`(b)/(2)` + c = 0

And

4
`c^(2)` + bc + c = 0

c(4c + b + 1) = 0

Let's say that 4c + b + 1 = 0

b = -1 - 4c

1 +
`(-1-4c)/(2)` + c = 0

`(1)/(2)` - 2c + c = 0

So c = 0.5 but c can't be 0.5 as one of the roots is 0.5 and c is another so 4c + b + 1 ≠ 0 meaning c = 0 from our second equation

1 +
`(b)/(2)` + 0 = 0

2 + b = 0

b = -2