If $\alpha $ and $\beta $ are zeros of the quadratic polynomial $2x^2+3x-6$, then find the values of : $\alpha^2+\beta^2$

Using the relationship between zeros and coefficients, we find the sum of the roots alpha + beta = -3/2 and the product of the roots alpha * beta = -6/2 = -3. We use the algebraic identity alpha^2 + beta^2 = (alpha + beta)^2 - 2(alpha * beta) to find the required value. Substituting the known values gives (-3/2)^2 - 2(-3), which equals 9/4 + 6. This simplifies to 9/4 + 24/4, resulting in 35/4.

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