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Degree: Mathematics with Study in Continental Europe (Masters) - Bristol University
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To find the roots, we solve the equation 3x2 + 13x + 4 = 0.
We could try factorising the equation, which gives us
(3x + 1)(x + 4) = 0
So the roots are x = -1/3 and x = -4.
Alternatively, we could use the quadratic formula;
x = (-b +/- sqrt( b2 - 4ac)) / 2a
[note that sqrt(x) is the square root of x]
x= (-13 +/- sqrt(132 - 4*3*4)) / 2*3
= (-13 +/- sqrt(169 - 48)) / 6
= (-13 +/- sqrt(121)) / 6
= (-13 +/- 11) / 6
= (-13 + 11) / 6 or (-13 - 11) / 6
= -2 / 6 or -24 / 6
= -1 / 3 or -4
So again, the roots are x = -1 / 3 or x = -4.see more