Question

The coefficients b and c in the equation x² + bx + c = 0 are also the roots of that equation (c ≠ 0). Find the values of b and c.

Answer 1

The values of b and c in the equation x² + bx + c = 0 where b and c are also the roots are b² = -c/2.

Step-by-step explanation:

In this equation, x² + bx + c = 0, we are given that the coefficients b and c are also the roots of the equation.

By substituting b and c into the equation, we get:

x² + bx + c = 0

(b)² + b(b) + c = 0

b² + b² + c = 0

2b² + c = 0

Since c ≠ 0, we can divide the equation by c:

2b²/c + c/c = 0/c

2b²/c + 1 = 0

2b²/c = -1

2b² = -c

b² = -c/2

Therefore, the values of b and c are such that b² = -c/2.