What is the value of a such that the equation (3a+1)x2 + (a+2)x + 1 = 0 shall have equal roots.

To solve these problems, we use the concept of the discriminant of a quadratic equation $Ax^2 + Bx + C = 0$. The discriminant is given by $\Delta = B^2 - 4AC$.

• For equal roots, $\Delta = 0$.
• For real roots, $\Delta \ge 0$.

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1. What is the value of $a$ such that the equation $(3a+1)x^2 + (a+2)x + 1 = 0$ shall have equal roots.

Step 1: Identify the coefficients A, B, and C from the given quadratic equation.
The equation is $(3a+1)x^2 + (a+2)x +