What are the roots of 3x^2 + 13x + 4 ?

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]

So here;

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.

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