CBSE · Class 10 · Mathematics · PolynomialsFind a quadratic polynomial whose zeroes are $2$ and $-3$.

Let the zeroes of the required quadratic polynomial be $\alpha = 2$ and $\beta = -3$. First, we can calculate the sum of these zeroes: $\alpha + \beta = 2 + (-3) = -1$. Next, we calculate their product: $\alpha \beta = (2)(-3) = -6$. Using the standard quadratic polynomial formula constructed from the sum and product of zeroes, we have $P(x) = x^2 - (\alpha + \beta)x + \alpha \beta$. Substituting our calculated values gives $P(x) = x^2 - (-1)x + (-6)$, which simplifies directly to the final polynomial expression $x^2 + x - 6$.