A quadratic equation $$x^2 + bx + 12 = 0$$ has 2 as one of its roots, and another quadratic equation $$x^2 + bx + q = 0$$ has equal roots. Determine the value of $$b$$.

Question

Accepted Answer

To solve the problem, consider the first quadratic equation $$x^2 + bx + 12 = 0$$. Since 2 is one of its roots, substitute $$x = 2$$ into the equation. This gives:

$$
2^2 + b \cdot 2 + 12 = 0
$$

Simplify to get:  
$$
4 + 2b + 12 = 0
$$

Combine terms:  
$$
2b + 16 = 0
$$

Solve for $$b$$:  
$$
b = -8
$$

Thus, the value of $$b$$ is $$-8$$.

Answer

Answer

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