Sangeetha Pulapaka
The roots you got for the quadratic equation 3q^{2} + 6q - 1 = 0 are correct. The answer in the answer key must be related to a different set of quadratic equations. Let us find out what they are. So since the first set of roots are \approx- 0.18,-1.82. We round it off to -0.19 and -1.9. Let these roots be \alpha,\beta . The general form of a quadratic equation is x^{2} -(\alpha+\beta)x +\alpha\beta. The sum of roots is \alpha+\beta = -0.19 -1.9 = -2.09 and the product of the roots is \alpha\beta = 0.361 So x^{2} +2.09 x +0.361 = 0 is the quadratic equation . We can recheck the same by using the quadratic formula \frac{-b\pm\sqrt{b ^2-4ac}}{2a} substituting the values of a,b and c in this formula we get the same roots as before.