1.2 If 2 and -4 are the rots of the equation $$ x^{2}+b x+c=0 $$ Determine the values of $$ b $$ and $$ c $$.

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1. Given the quadratic equation  
   $$
   x^2 + bx + c = 0
   $$  
   with roots $$2$$ and $$-4$$.

2. We use Vieta's formulas which state that for a quadratic equation:  
   - The sum of the roots is  
     $$
     r_1 + r_2 = -b
     $$
   - The product of the roots is  
     $$
     r_1 \cdot r_2 = c
     $$

3. Substitute the given roots $$r_1 = 2$$ and $$r_2 = -4$$:
   - Sum:  
     $$
     2 + (-4) = -2 \quad \Rightarrow \quad -b = -2
     $$
     Solving for $$b$$:
     $$
     b = 2
     $$
   - Product:  
     $$
     2 \cdot (-4) = -8 \quad \Rightarrow \quad c = -8
     $$

4. Therefore, the values of the coefficients are:  
   $$
   b = 2 \quad \text{and} \quad c = -8.
   $$
$$ b = 2 $$ and $$ c = -8 $$.

1.2 If 2 and -4 are the rots of the equation \( x^{2}+b x+c=0 \) Determine the values of \( b \) and \( c \).

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