Finding the Value of C and Solving for Roots in a Quadratic Equation

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To find the value of C in the quadratic equation f(x) = 6x² + 12x + c, the discriminant must equal zero for equal roots, leading to the equation 144 - 24c = 0, which simplifies to c = 6. For part b, solving the equation f(x) = 0 with c = 6 results in 6x² + 12x + 6 = 0, which factors to (x + 1)(6x + 6) = 0, yielding the root x = -1. The quadratic formula could also be applied for verification, confirming the solution is correct. The calculations were validated by other participants in the discussion.
discombobulated
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ok this is the question:

f(x) = 6x2 + 12x + c where C is a constant.
a) Given f(x) =0 has equal roots, find the value of C.

so this what i did for this part:

b2- 4ac = 0 (formula for discriminant)
122-4(6xC) =0
144-24c=0
6-C=0
c=6 (is that right?)

Now for the next part:
b) Hence, solve f(x) = 0

6x2+12x+6=0
(x=1)(6x+6)=0
x=-1 x= -6/6 = -1

I wasn't really sure what i was doing but i tried to work it out and this is what i did but I'm not sure if it's right. (i don't think it is!) Can somebody help please!
 
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a) Correct.
b) I would've used the quadratic formula. It's correct, though.
 
really? wow i was convinced it was wrong, thanks!
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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