Question

Please Help!

(I have had trouble with this question for a while.)

The difference of the roots of the quadratic equation
`x^2+bx+c` is
`|b-2c|` . If
`c \\eq 0`, then find
`b` in terms of
`c`.

Answer 1

Below

Explanation:

The equation is x2 + bx + c

The coefficients are

● a = 1

● b

● c is the constant

The difference of the roots is | b - 2c |

Let s and p be the roots of the polynomial

● s - p = | b - 2c | (1)

● s + p = -b/a => s + p = -b (2)

(1) + (2)

● s - p + s + p = |b-2c| - b

● 2s = | b - 2c | - b

● 2s = b - 2c - b or 2s = 2c - b - b

● 2s = - 2c or 2s = 2c - 2b

● s = - c or s = c - b

We want to express b in term of c. So we will be intetsted in the 2nd equation

● s = c - b

● s - c = - b

● b = c - s