Question

If one zero of the polynomial \( (a+2)x^2 - 3ax -2 \) is negative of the other, then find the polynomial.

Hint:

For opposite roots, sum of roots must be zero.

Answer 1

Let the roots be \( \alpha \) and \( -\alpha \).
Sum of the roots:
\[ \alpha + (-\alpha) = 0 = -\frac{-3a}{a+2}. \] \[ \Rightarrow \frac{3a}{a+2} = 0 \Rightarrow 3a = 0 \Rightarrow a = 0. \] Thus, the polynomial simplifies to:
\[ (x^2 - c^2). \]