Solve the equation 3a^2+4a+1=3 for all values of a. Give your answers to 3 significant figures.
First take the 3 over the other side to make the right hand side zero, turning it into a homogeneous equation: 3a2+4a-2=0. Since the expression on the left hand side cannot be factorised, we have to use quadratic formula. Applying the quadratic formula gives the following solutions for a: a1= (-4 + sqrt(42 - (4 x 3 x -2)))/ (2 x 3) = (-4 + sqrt(40) / 6 = 0.3874... and a2= (-4 - sqrt(42 - (4 x 3 x -2)))/ (2 x 3) = (-4 - sqrt(40) / 6 = -1.7207... . Hence, final solutions are a = 0.387 and a = -1.72.
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